U.S. patent application number 15/442370 was filed with the patent office on 2017-06-08 for integrative software system, device, and method.
This patent application is currently assigned to Physical Optics Corporation. The applicant listed for this patent is Physical Optics Corporation. Invention is credited to Thomas Forrester, Joanna Jannson, Tomasz Jannson, Andrew Kostrzweski, Thomas Nielsen, Christian Veeris, Wenjian Wang.
Application Number | 20170161625 15/442370 |
Document ID | / |
Family ID | 58798426 |
Filed Date | 2017-06-08 |
United States Patent
Application |
20170161625 |
Kind Code |
A1 |
Jannson; Tomasz ; et
al. |
June 8, 2017 |
INTEGRATIVE SOFTWARE SYSTEM, DEVICE, AND METHOD
Abstract
A non-transitory computer readable medium for storing one or
more sequences of one or more instructions for execution by one or
more processors in a processing system to perform a method for
determining a dichotomy for a parametric decision process, the
instructions when executed by the one or more processors are
presented. Embodiments can be configured to define a network having
a plurality of members as inter-member coherency coupling
represented by elements of a coherency matrix, wherein for each
i.sup.th member the network includes an intensity value, I.sub.i.
Further embodiments may include determining non-diagonal elements
T.sub.ij of the coherency matrix in which i.noteq.j and in which i
and j represent i.sup.th and j.sup.th members of the network, and
constructing diagonal kernels K.sub.i or non-diagonal kernels
H.sub.i based on the non-diagonal elements T.sub.ij of the
coherency matrix and intensity values (I.sub.i) of the members.
Inventors: |
Jannson; Tomasz; (Torrance,
CA) ; Wang; Wenjian; (Torrance, CA) ;
Forrester; Thomas; (Hacienda Heights, CA) ;
Kostrzweski; Andrew; (Garden Grove, CA) ; Jannson;
Joanna; (Torrance, CA) ; Nielsen; Thomas;
(Torrance, CA) ; Veeris; Christian; (Torrance,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Physical Optics Corporation |
Torrance |
CA |
US |
|
|
Assignee: |
Physical Optics Corporation
Torrance
CA
|
Family ID: |
58798426 |
Appl. No.: |
15/442370 |
Filed: |
February 24, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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14147247 |
Jan 3, 2014 |
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15442370 |
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61780695 |
Mar 13, 2013 |
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61808514 |
Apr 4, 2013 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06N 7/005 20130101 |
International
Class: |
G06N 7/00 20060101
G06N007/00; G06F 17/16 20060101 G06F017/16 |
Claims
1. A non-transitory computer readable medium storing one or more
sequences of one or more instructions for execution by one or more
processors in a processing system to perform a method for
determining a dichotomy for a parametric decision process, the
instructions when executed by the one or more processors, cause the
one or more processors to perform the operations of: defining a
network having a plurality of members an inter-member coherency
coupling represented by elements of a coherency matrix, wherein for
each i.sup.th member the network includes an intensity value,
I.sub.i; determining non-diagonal elements T.sub.ij of the
coherency matrix in which i.noteq.j and in which i and j represent
i.sup.th and j.sup.th members of the network, respectively;
constructing diagonal kernels K.sub.i or non-diagonal kernels
H.sub.i based on the non-diagonal elements T.sub.ij of the
coherency matrix and intensity values (I.sub.i) of the members.
2. The non-transitory computer readable medium of claim 1, wherein
for a given i.sup.th member, defining a diagonal kernel vector as a
function of its diagonal kernel vector K.sub.i and a unit vector
as: {right arrow over (K)}.sub.i=K.sub.i.
3. The non-transitory computer readable medium of claim 2, wherein
{circumflex over (k)}.sub.i is given by: {circumflex over
(k)}.sub.i=b.sub.x .sub.x+b.sub.y .sub.y+b.sub.z .sub.z in which |
.sub.x|=| .sub.y|=| .sub.z|=1; .sub.x .sub.y=0; .sub.x .sub.z=0;
.sub.y .sub.z=0 and
b.sub.x.sup.2+b.sub.y.sup.2+b.sub.z.sup.2=1.
4. The non-transitory computer readable medium of claim 2, wherein
for the given i.sup.th member, defining a parametric decision
vector, {right arrow over (S.sub.i)}, as a function of parametric
decision scalar S.sub.i, and unit vector, , as: {right arrow over
(S)}.sub.i=S.sub.i.
5. The non-transitory computer readable medium of claim 2, wherein
is given by: s.sub.i=a.sub.x .sub.x+a.sub.y .sub.y+a.sub.z .sub.z
in which | .sub.x|=| .sub.y|=| .sub.z|=1; .sub.x .sub.y=0; .sub.x
.sub.z=0; .sub.y .sub.z=0 and
a.sub.x.sup.2+a.sub.y.sup.2+a.sub.z.sup.2=1.
6. The non-transitory computer readable medium of claim 4, wherein
the operation further comprises determining a moral skew factor for
the ith network member as cos .theta..sub.i in which {right arrow
over (S.sub.i)}{right arrow over (K.sub.i)}=S.sub.iK.sub.i cos
.theta..sub.i.
7. The non-transitory computer readable medium of claim 1, wherein
wherein the operations further comprise calculating a strength of
diagonal kernels K.sub.i as: K i = j = 1 N T ij I i I j .
##EQU00047## In which I.sub.j is the intensity value of the
j.sup.th member of the network.
8. The non-transitory computer readable medium of claim 1, wherein
the operations further comprise calculating a decision weighted
mean, <S>, based on diagonal kernels K.sub.i as: S = i = 1 N
S i K i i = 1 N K i . ##EQU00048##
9. The non-transitory computer readable medium of claim 1, wherein
the operations further comprise calculating an i.sup.th-weight as w
i = K i i = 1 N K i ; 0 .ltoreq. w i .ltoreq. 1 , and i = 1 N w i =
1. ##EQU00049##
10. The non-transitory computer readable medium of claim 1, wherein
the members comprise an individual, a high-value-individual
candidate, or a group of interest.
11. The non-transitory computer readable medium of claim 1, wherein
matrix elements are non-symmetrical, such that
T.sub.ij.noteq.T.sub.ji.
12. The non-transitory computer readable medium of claim 1, wherein
Tij is defined as: Tii=1, and Tij.ltoreq.1.
13. A non-transitory computer readable medium storing one or more
sequences of one or more instructions for execution by one or more
processors in a processing system to perform a method for
determining a moral skew factor for a parametric decision process,
the instructions when executed by the one or more processors, cause
the one or more processors to perform the operations of: defining a
network having a plurality of members in which each member
comprises an intra-ego influence including a first unit vector,
{circumflex over (k)}, and an inter-ego influence including a
second unit vector, s, representing a member strength, constructing
first and second kernel vectors parallel to said first and second
unit vectors, respectively; computing an angle, .theta., between
the first and second kernel vectors; and determining the moral skew
factor as cos(.theta.).
14. The non-transitory computer readable medium of claim 13,
further comprising determining an inter-member coherency coupling
represented by elements of a coherency matrix, wherein each
i.sup.th member the network includes an intensity value,
I.sub.i.
15. A non-transitory computer readable medium storing one or more
sequences of one or more instructions for execution by one or more
processors in a processing system to perform a method for
determining a moral skew factor for a parametric decision process,
the instructions when executed by the one or more processors, cause
the one or more processors to perform the operations of: defining a
network having a plurality of members an inter-member coherency
coupling represented by elements of a coherency matrix, wherein for
each i.sup.th member the network includes an intensity value,
I.sub.i; determining non-diagonal elements R.sub.ij of the
coherency matrix in which i.noteq.j and in which i and j represent
i.sup.th and j.sup.th members of the network, respectively;
determining a non-diagonal pseudo-vector, {right arrow over
(G)}.sub.i, for the i.sup.th member; determining a parametric
decision vector, {right arrow over (S)}.sub.i, for the i.sup.th
member; computing an angle, .theta., between the non-diagonal
pseudo-vector and parametric decision vector; and determining the
moral skew factor as cos(.theta.).
16. The method of claim 15, wherein the operations further comprise
determining a projection of non-diagonal pseudo-vector, {right
arrow over (G)}.sub.i, onto parametric decision vector, {right
arrow over (S)}.sub.i, and computing a non-normalized weight of the
parametric decision vector as a sum of the projection and the
intensity I.sub.i for that member.
17. The method of claim 16, wherein the operations further comprise
determining whether a member is a high-value member based on the
moral skew factor and the non-normalized weight.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional application of U.S. patent
application Ser. No. 14/147,247, filed Jan. 3, 2014, which claims
the benefit of U.S. Provisional Application Nos. 61/780,695, titled
Bayesian Inter-cloud Coherency System and Method and filed on Mar.
13, 2013; and 61/808,514, titled Bayesian Inter-cloud Coherency
System and Method and filed on Apr. 4, 2013.
TECHNICAL FIELD
[0002] The present invention relates generally to detection and
prediction systems, and more particularly, some embodiments relate
to systems and methods for adverse network detection.
DESCRIPTION OF THE RELATED ART
[0003] Conventional Artificial Intelligence (AI) software systems
used to identify adverse networks, such as organized crime
networks, or IED (Improvised Explosive Device) networks, for
example, are typically based on some kind of statistical passive
code analysis and machine learning solution. Others use computer
database structurization. In general, such software systems can be
either "probabilistic," or "logicist," or some combination of both.
In the case of probabilistic networks, such as Bayesian networks,
for example, the usual challenge faced is the "actionality"
problem--i.e., actional impotency. That is, although data knowledge
is collected by such systems, there is no action methodology
leading to a machine-learned conclusion or result. On the other
hand, in the case of logicist networks, there are often
contradictions and difficulties separating hard facts (e.g., facts
that must be true) from soft facts (e.g., data or information that
may be true).
[0004] In addition, conventional approaches using AI systems not
only suffer from the division between probabilistic and logicist
approaches to AI, but also from a controversy between Bayesian and
Dempster-Shafer inferences. Bayesian inferences are generally used
for exclusive events, while Dempster-Shafer inferences are
generally used for correlated events, respectively. Furthermore,
there is a fundamental challenge between correlation and causation
of facts. A still further challenge arises when dealing with
non-monotonic events (i.e., events contradictory to previous
experience).
[0005] Historically, artificial intelligence and intelligent
computing have been verified by the so-called Turing's test; i.e.,
a successful intelligent machine (computer) communicating with a
human (either by voice, by playing some game, or in some other way)
should be not recognizable from communication between humans. So
far, several machines have passed the Turing test, including the
IBM computer "Deep Blue" as a champion-level chess player, as well
as a number of machine-learned card players (in hearts, bridge,
etc.). In medicine, computer-based network structures based on
binary databases have been developed to evaluate patient symptoms
and diagnose conditions. Based on sophisticated mathematics and
Monte Carlo simulations, these networks have been able to identify
hidden variables in the causal chain. They have been restricted to
a very limited number of variables, however.
[0006] More success has been achieved using neural networks with
the ability for effective pattern recognition. These, for example,
are systems based on training of synaptic weights. Such training,
however, has been based on "black box" principles with no insight
to synaptic buildup internal mechanisms.
[0007] Therefore, although AI machine-learning has been successful,
its successes have been somewhat limited to rather narrow context
cases, where the Concept of Operations (CONOPS), or the field of
application has been heavily restricted. One of the typical
difficulties encountered is a difficulty correlating between
various causes. This has led to a redundancy problem with elements
such as: improper handling of bidirectional inference; difficulties
in retracting conclusions (due to non-monotonic events, for
example); improper treatment of correlated sources of evidence,
etc. In parallel, however, recent technological advances in
parallel computation, natural language processing (NLP), and in
object-oriented computer languages, such as: C++ and Java, have
stimulated interest in viewing a network not merely as passive code
for sorting factual knowledge, but also as a computational
architecture (heuristic) reasoning about that knowledge.
BRIEF SUMMARY OF THE EMBODIMENTS
[0008] The technology disclosed herein relates to Integrative
Software System (ISS) technology, which in various embodiments
combines two AI schools: probabilistic and logicist, together with
Bayesian Inference and Binary Sensing, in the form of Bayesian
Truthing Inference (BTI). The ISS, which can include digital
decision generation tools, can be configured to detect, recognize
and identify adverse networks by detecting Bayesian anomalous
events, or BAEVENTS, in cyberspace, through the inspection of
professional (or pseudo-professional) databases, or PRO-CLOUDS
(could also be referred to as "CYBER-CLOUDS").
[0009] In various embodiments, a discrete truthing space can be
included with targets that might be of interest--referred to as
High Value Individual Candidates (HVICs)--as sample units, and
targets that are confirmed by the system as targets of
interest--referred to as High Value Individuals (HVIs). In the
examples provided herein, these targets can be individuals (e.g.,
people), while in other embodiments, targets can be other entities.
Various embodiments can be configured to evaluate data and
information about HVICs to determine whether they are actually
HVIs.
[0010] The ISS architecture can, in some embodiments, be configured
as a chain structure with elemental tasks as its nodes. It can be
configured with two or more software engines. For example, in the
case of two engines, one may be an intra-cloud engine, and the
other an inter-cloud engine. In various embodiments, these can be
supported by multiple (e.g., 2, 3, 4, a dozen, or more) supportive
elemental tasks (modules).
[0011] The ISS chain can be fully actionable and can be configured
to avoid the correlation/causation contradiction by applying a
natural binary sensor scheme that is unidirectional, with a
well-defined causation relation. This scheme can be based
exclusively on sensor events and readouts (thus, avoiding
correlation problems). There can also be an intra-cloud software
engine (e.g., to select HVIs as yellow alarms), in parallel with a
2.sup.nd inter-cloud graph (software) engine for selecting cyber
networks. Such cyber networks can be, for example, in the form of
graphitis (defined in Section 2.2).
[0012] A Compound Association Identifier (CAI) can be included to
identify parameters of interest (e.g., cyberphone numbers or other
parameters) obtained from multiple engines, in parallel, as
belonging to the same target candidates (e.g. for the same HVIC).
For example, multiple engines working in parallel evaluating
different data (e.g. 1 intra-cloud and the other inter-cloud) using
different inferences can arrive at the same conclusion that a
target candidate is one of interest. This can result in a target
candidate being identified as a target or high value individual. In
some embodiments, when this occurs, this can result in a red-alarm,
or a flag associated with that individual, or other alert. In other
embodiments, a higher level of alert may be required before
reaching such a red-alarm state. In such embodiments, the alert
generated as a result of 2 engines working in parallel may be an
orange alarm or other mid-level alert. As will be apparent to one
of ordinary skill in the art after reading this description,
multiple levels of alarms can be utilized depending on the level of
correlation.
[0013] The ISS can, in some embodiments, be fully autonomous, or
semi-autonomous. The semi-autonomous system can be implemented
working with the help of experts. The ISS intra-cloud software
engine can be configured to work with the support of
Object-Oriented-Rules (OORs), which in various embodiments are
mini-computer-programs, developed in an Object-Oriented-Language
such as Java, C++, or others.
[0014] Both engines can also be configured to work with the support
of two novel computer tools: a Network Synthesizer System (NSS),
and a Context-based Synonymous Object (CONSYN) scheme. While the
OORs are non-heuristic, they can produce intra, or inter columns of
daughter-OORs, or DOORs, which as heuristic OORs, can be developed
semi-automatically, or automatically. The ISS can also be
configured to provide automatic machine (heuristic) learning, as
well as intra-cloud and inter-cloud feedback to maximize system
performance, by minimizing its cost function using basic Bayesian
Figures of Merit, such as, for example Positive Predictive Value
(PPV). This training process can be provided in a macroscopic and
microscopic way, the latter avoiding "black box" limitation. In
addition to the above outer (inter-network) concept, the novel
complementary inner (intra-network) concept can also be
addressed.
[0015] PPVs can be automated (e.g., based on past information and
positive hits, without human intervention), or they may be based at
least in part on human-supplied information, such as, for example,
a human score. PPV scores can provide a `confidence factor` in the
identification of an HVIC as an HVI.
[0016] Inner Networks.
[0017] It should be noted that the adverse networks, such as
terrorist and organized crime networks, represent groups that are
non-adverse from an intra-group perspective. That is, within the
group the members are not typically adverse to one another. From
this perspective, they can be considered as inner networks, where
the decision process modeling is important. This is also addressed
by the technology disclosed herein, based on a so-called moral skew
factor, and parametric decision process, as explained in Sections
1, 3 and 7, and in FIG. 48 and Table 1.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The present invention, in accordance with one or more
various embodiments, is described in detail with reference to the
following figures. The drawings are provided for purposes of
illustration only and merely depict typical or example embodiments
of the invention. These drawings are provided to facilitate the
reader's understanding of the invention and shall not be considered
limiting of the breadth, scope, or applicability of the invention.
It should be noted that for clarity and ease of illustration these
drawings are not necessarily made to scale.
[0019] Some of the figures included herein illustrate various
embodiments of the invention from different viewing angles.
Although the accompanying descriptive text may refer to specific
spatial orientations, such references are merely descriptive and do
not imply or require that the invention be implemented or used in a
particular spatial orientation unless explicitly stated
otherwise.
[0020] FIG. 1 is a diagram depicting an exemplary Integrative
Software System logic scheme with an intra-cloud engine and a
graphiti engine.
[0021] FIG. 2 is a diagram depicting exemplary graphitis.
[0022] FIG. 3 is a diagram depicting Bayesian inter-cloud
coherency.
[0023] FIG. 4 is a diagram depicting an Integrative Software System
chain structure with an intra-cloud engine and an inter-cloud
engine.
[0024] FIG. 5 is a diagram depicting a heuristic learning chain
sub-structure.
[0025] FIG. 6 is a diagram depicting an intra-cloud engine
producing output using a plurality of cybersensors and associated
readout sub-modules.
[0026] FIG. 7 is a diagram depicting two exemplary High Value
Individual (HVI) recommendation processes based on Figure of Merit
(FoM) values.
[0027] FIG. 8 is a diagram depicting AND and OR logic operations
using set theory.
[0028] FIG. 9 is a diagram depicting OR and XOR logic operations
using Boolean algebra.
[0029] FIG. 10 is a diagram depicting modulo-algebras, including:
(a) an example of modulo-2 (Boolean) algebra; and (b) an example of
modulo-7 algebra.
[0030] FIG. 11 is a diagram depicting an exemplary process creating
a Daughter Object-Oriented Rule (DOOR) by applying Boolean logic to
Object-Oriented Rules (OORs).
[0031] FIG. 12 is a diagram depicting another exemplary process
creating a Daughter DOOR by applying Boolean logic to OORs.
[0032] FIG. 13 is a diagram depicting an exemplary process creating
a DOOR by applying Boolean logic to two other DOORs and an
equivalent logic circuit.
[0033] FIG. 14 is a diagram depicting a Context-based Synonymous
Object (CONSYN) sub-system and algorithm.
[0034] FIG. 15 is a diagram depicting a Network Synthesizer System
(NSS) structure at a 1.sup.st layer and a 2.sup.nd layer of
description.
[0035] FIG. 16 is a diagram depicting a NSS structure at a 3.sup.rd
layer of description.
[0036] FIG. 17 is a diagram depicting an exemplary compound
association process.
[0037] FIG. 18 is a chart depicting an exemplary time event
correlation.
[0038] FIG. 19 is a graph depicting an exemplary social
network.
[0039] FIG. 20 is a coherency matrix for N=3.
[0040] FIG. 21 is a graph depicting normal parametric order for
N=3.
[0041] FIG. 22 is a graph depicting normal parametric order.
[0042] FIG. 23 is a graph depicting the NPO (Normal Parametric
Order) case for N=3.
[0043] FIG. 24 is a coherency matrix with elements defined by
equations 21a-c.
[0044] FIG. 25 is a diagram depicting inter-group coherency.
[0045] FIG. 26 is a diagram depicting causation for a Binary
Sensor.
[0046] FIG. 27 is a graph depicting the Bayesian Paradox.
[0047] FIG. 28 is a diagram depicting Bayesian truthing sets.
[0048] FIG. 29 is a diagram depicting a Lossless Multi-Alarm (LMA)
method.
[0049] FIG. 30 is a graph depicting (a) Positive Predictive Values
(PPVs) over time and (b) a Cost Function (CF) over time during a
training process.
[0050] FIG. 31 is a diagram depicting a dual engine connection
method.
[0051] FIG. 32 is graph depicting an example of a relation between
i-indexing and l-indexing during a parametric decision process.
[0052] FIG. 33 is a diagram depicting multi-dimensional decision
space generalizations from: (a) single parametric space into (b) a
multitude of parametric spaces.
[0053] FIG. 34 is an example (RISK)-parametric decision scale.
[0054] FIG. 35 is a diagram depicting an exemplary parametric
ensemble.
[0055] FIG. 36 is a diagram depicting a simple parametric
prognosis.
[0056] FIG. 37 is a diagram depicting a logic structure for a
Parametric Cost Function (PCF) construction.
[0057] FIG. 38 is a diagram depicting a logic structure for
Parametric Intensity Prognosis.
[0058] FIG. 39 is a diagram depicting a Parametric Decision
Ensemble (PDE) architecture.
[0059] FIG. 40 is a diagram depicting PDE phenomenology.
[0060] FIG. 41 is a diagram depicting a thermodynamics gas analogy
to a PDE.
[0061] FIG. 42 is a diagram depicting a comparison in 2D-space of:
(a) a PDE orthogonal base and (b) a non-orthogonal base.
[0062] FIG. 43 is a diagram depicting a scales product of two
parametric decision vectors.
[0063] FIG. 44 is a diagram depicting a parametric decision and
kernel unit vectors' scalar product defined in orthogonal unit
vector base.
[0064] FIG. 45 is a diagram depicting a parametric decision and
kernel unit vectors' scalar product defined in non-orthogonal unit
vector base.
[0065] FIG. 46 is a graph depicting quantitative analysis of a
moral skew factor.
[0066] FIG. 47 is a diagram depicting network inner coherency.
[0067] FIG. 48 is a graph depicting geometric modeling of
non-diagonal kernel vector algebra.
[0068] FIG. 49 is a diagram illustrating an exemplary computing
module that may be used to implement any of the embodiments
disclosed herein.
[0069] The figures are not intended to be exhaustive or to limit
the invention to the precise form disclosed. It should be
understood that the invention can be practiced with modification
and alteration, and that the invention be limited only by the
claims and the equivalents thereof.
DETAILED DESCRIPTION
TABLE-US-00001 [0070] Table of Contents Section 1: ISS Inner and
Outer Network Structures 17 1.1 Network Inner and Outer Structures
Summary 17 1.1.1 The Importance of Outer and Inner Network
Structures 17 1.1.2 An example role for the Moral Skew Factor Help
in 18 Network Surveillance 1.1.3 Use of a Parametric Decision 19
1.1.4 Differentiation Between the Coherency Matrix and the 19 Moral
Skew Factor 1.1.5 Role of Inter-Ego and Intra-Ego Kernel Elements
20 1.1.6 Role of Correlation (Coherence) and Experts in Inner and
20 Outer Network Structures 1.1.7 Geometry of Non-Diagonal Kernel
Algebra 21 1.1.8 Role of Mathematics in the Integrative Software
System (ISS) 23 1.1.9 Reduction and Re-Normalization of Unit Vector
Bases 23 1.1.10 Radicalization Level as Decision Parameter 24
1.1.11 Comparison Summary 25 Section 2: Example ISS Concepts,
Components and Architecture (Outer 26 Network) 2.1 ISS Logic Scheme
26 2.2 Graphitis 27 2.3 System Architecture 28 2.4 ISS Cyberspace,
Truthing (Sample) Space and System Envelope 29 Section 3: Example
System Chain Structure (Outer and Inner Network) 31 3.1 System
Chain Structure 31 3.2 System Engines and Feedback 33 3.3
Intra-Cloud Engine Set 34 3.4 HVI Recommendation Process 35 3.5
Object-Oriented Rules 38 3.6 DOORs based on AND-operation 40 3.7
Context-Based Synonymous Object 42 3.8 Link Analysis (Network
Synthesizer System) 45 3.9 Compound Association Identifier and
Identification (ID) Method 47 3.10 Clock Anomaly 48 3.11 Parametric
Decision and Coherent Coupling 50 3.11.1 Mathematical Model 52
3.11.2 Anomalous Coupling 57 3.11.3 Dynamic Coupling 58 3.11.4
Inter-Group Coupling 59 Section 4: Bayesian Truthing Inference
(Outer Network) 60 4.1 Bayesian Inference and Binary Sensors 60 4.2
Positive Predictive Value and Bayesian Paradox 62 4.3 Bayesian
Truthing 64 4.3.1 Truthing Sampling Space 64 4.4 Bayesian Truthing
Theorem (BTT) 67 4.5 Analogy between X-Ray Luggage Inspection and
the ISS 68 4.6 Numerical Examples Illustrating ISS Bayesian
Truthing 69 4.7 Relations Between Non-Diagonal Statistical and
Truthing 72 Parameters 4.8 Lossless Multi-Alarm Method 74 Section
5: System Performance Components (Outer Network) 75 5.1 Cost
Function 75 5.2 System Feedback 77 5.3 Dual Engine Connection 78
Section 6: Network Inner Coherency (Inner Network) 80 6.1 Inner
Network Coherency 80 6.2 Comparison of Diagonal and Non-Diagonal
Kernel Vectors 82 6.3 Moral Skew Effect and Psychoanalysis 83
Section 7: Inner Network Analysis (Inner Network) 84 7.1
Inter-Adverse vs. Intra-Friendly 84 7.2 Parametric Statistical
Ensemble 85 7.3 Parametric Prognosis 89 7.3.1 Parametric Intensity
Prognosis 90 7.4 Coherent Coupling Engineering 91 7.5 Application
Scenarios for PDE Systems 94 7.6 Phenomenology of PDE System 99
7.6.1 Origin of the systems and methods described herein 99 7.6.2
Thermodynamic Gas Analogy 101 7.6.3 Moral Sociology Analogy 104 7.7
Moral Skew Factor 106 7.7.1 Inter-Ego vs. Intra-Ego 106 7.7.2 Unit
Vector Bases 107 7.7.3 Primary Color Analogies 107 7.7.4 Scalar
Product of Parametric Decision and Kernel Unit 108 Vectors 7.7.5
Scalar Product of Parametric Decision and Kernel Vectors 110 7.7.6
Diagonal and Non-Diagonal Kernel Vectors 110 7.7.7 Quantitative
Analysis of the Moral Skew Factor 114 Section 8: Example Computer
Program Product Embodiments 116
[0071] Section 1: ISS Inner and Outer Network Structures
[0072] 1.1 Network Inner and Outer Structures Summary
[0073] This Section discusses both inner and outer network
structures, which can be viewed in some contexts as "different
sides of the same coin." The outer and inner network structures are
each discussed in greater detail in later Sections of this
document.
[0074] 1.1.1 the Importance of Outer and Inner Network
Structures
[0075] As described above, although adverse (or, hostile) networks
such as terrorist and organized crime networks may be externally
adverse, internally, they may not be adverse because the network
members often cooperate among themselves to achieve their
objectives. Therefore, any network, whether or not adverse, has
some internal dynamics, which can influence its efficiency. In
particular, a higher level of coherency between adverse-network
members typically leads to a more successful network operation.
Also, surveillance of such adverse networks may be difficult due to
legal constraints. Accordingly, an understanding of the motivation
of network members (Groups of Interest, or individuals) typically
does help in network surveillance and improves prognostics of their
action. The Inner Network structure taxonomy typically includes a
network (group) and network members. As also described above, the
network members may be either individuals, or sub-groups referred
to as Groups of Interest (GOIs).
[0076] 1.1.2 an Example Role for the Moral Skew Factor Help in
Network Surveillance
[0077] As stated above, "people see us differently from how we see
ourselves." Therefore, processes in various embodiments can be
implemented with an understanding as to why people make certain
decisions (preferably, without asking them about it). Accordingly,
with this understanding, the system can better predict the actions
of these individuals in general, and some hostile operations, in
particular. The moral skew factor is a mathematical tool that may
be used to predict, or better prognose such decision. This can be
accomplished, for example, by adding a vectorial scalar product
into network coherence coupling modeling.
[0078] 1.1.3 Use of a Parametric Decision
[0079] The network decision process in various embodiments can be
difficult to present in mathematical form for a generalized case.
Therefore, to aid in the reader's understanding, it is presented
herein in terms of a specific context or example. By introducing a
Parametric Decision Ensemble (PDE) (i.e., by adding a statistical
ensemble, which specifies a class of decisions that can be
described by the same decision parameter), various embodiments can
be presented to preserve both specificity and maximum generality
within the network decision process.
[0080] 1.1.4 Differentiation Between the Coherency Matrix and the
Moral Skew Factor
[0081] The Moral Skew Effect (MSE) in general, and the moral skew
factor in particular, describe a moral dichotomy between the
Freudian super-ego (or ISS inter-ego) and the Freudian id (or ISS
intra-ego). This may be manifested in various embodiments by moral
tastes (or, senses), and self-interest tastes (or, senses). The
moral skew factor is defined as cos(.theta..sub.i) where
.theta..sub.i is the angle between unit vectors and {circumflex
over (k)}.sub.i in which s.sub.i represents a parametric decision,
S.sub.i, and {circumflex over (k)}.sub.i represents coherent
couplings. It can be assumed that s.sub.i is inclinated into
intra-ego (self-interest), while {circumflex over (k)}.sub.i is
inclinated into inter-ego moral senses (tastes). As such,
cos(.theta..sub.i) is projected, globally, onto all network
members, while coherency matrix elements, T.sub.ij, are specific
for each network member.
[0082] 1.1.5 Role of Inter-Ego and Intra-Ego Kernel Elements
[0083] Eq. (142) in Section 7.76, below, defines a non-diagonal
kernel vector, {right arrow over (H)}.sub.i, which is characterized
by two unit vectors, intra-ego-vector, s.sub.i, and
inter-ego-vector, {circumflex over (k)}.sub.i (the name
"non-diagonal" is related to "kernel," not to "vector"). The
scalar, G.sub.i, is described by both intra-ego intensities,
I.sub.i, and inter-ego non-diagonal coherency matrix elements,
R.sub.ij, as in Eq. (141), also in paragraph [0366].
[0084] 1.1.6 Role of Correlation (Coherence) and Experts in Inner
and Outer Network Structures
[0085] Because the outer network ISS structure may be either
automated or semi-automated, it is preferably configured to avoid
dichotomy between correlation and causation. Therefore, in various
embodiments it is based on a non-correlated binary sensor chain
structure in which anomalous events are separated from regular
events (binary sensors are based on exclusive (non-correlated)
events). The outer ISS system in various embodiments has two
separate software engines, the intra-cloud engine and the
inter-cloud engine. These can be configured, for example, such that
the 1.sup.st software engine does not avoid un-correlated events,
while the 2.sup.nd software engine uses correlated events.
[0086] In contrast, the inner network ISS structure is heavily
based on experts' involvement, which can be used, for example, to
determine T.sub.ij, and cos(.theta..sub.i)-values, in which
correlation, or coherent coupling is the predominant effect.
However, the role of experts is not necessarily supervisory and may
be advisory, while the network mathematical structure can be
configured to provide a supervision process itself.
[0087] 1.1.7 Geometry of Non-Diagonal Kernel Algebra
[0088] This mathematical section describes relationships between
geometry and algebra of a non-diagonal kernel, G.sub.i, defined by
Eq. (143), where the non-diagonal kernel pseudo-vector (the term
"pseudo" describes the fact that only part of the kernel {right
arrow over (H)}.sub.i vector is included, but {right arrow over
(G)}.sub.i is still a vector itself) {right arrow over (G)}.sub.i,
is:
{right arrow over (G)}.sub.i={circumflex over (k)}.sub.iG.sub.i
(1)
[0089] We also define the intensity vector, {right arrow over
(I)}.sub.i, which, according to Eq. (3), is
{right arrow over (I)}.sub.i=s.sub.iI.sub.i. (2)
[0090] We see that scalar product of these vectors, is
{right arrow over (G)}.sub.i{right arrow over
(I)}.sub.i={circumflex over
(k)}.sub.is.sub.iG.sub.iI.sub.i=G.sub.iI.sub.i cos .theta..sub.i
(3)
while non-normalized weight, W.sub.i, of the weighted average mean
of parametric decision, S.sub.i, has according to Eq. (141) the
following form:
W.sub.i=I.sub.i+G.sub.i cos .theta..sub.i=I.sub.1+G.sub.i.parallel.
(4)
where G.sub.i.parallel. is {right arrow over (G)}.sub.i-vector
projection onto s.sub.i-vector direction, as illustrated in FIG.
48. It is also evident from Eq. (141) that the normalized weight,
is
w i = W i i = 1 N ( I i + G i cos .theta. i ) ; i = 1 N w i = 1 ( 5
ab ) ##EQU00001##
[0091] In FIG. 48, an example of non-diagonal kernel vector
algebra, defined by Eqs. (1), (2), (3), (4), (5), (141), (142),
(143), (144), and (145) is shown. This geometry of non-diagonal
kernel vector algebra defines the non-normalized weight, 9000,
denoted as W.sub.i, which is the sum of non-diagonal kernel
pseudo-vector 9001, denoted as {right arrow over (G)}.sub.i,
projected into s.sub.i-direction and intensity scalar, 9002,
denoted as I.sub.i. The {right arrow over (G)}.sub.i-projection,
9003, is denoted as G.sub.i.parallel.. According to FIG. 48, we see
that the non-diagonal kernel vector, 9005, denoted as {right arrow
over (H)}, is less important than pseudo-vector, {right arrow over
(G)}, because, only {right arrow over (G)}-vector is projected to
parametric decision vector, 9006, (denoted as {right arrow over
(S)}.sub.i), by .theta..sub.i-angle, denoted as 9008. Higher weight
value, 9000, higher influence of ith-member on parametric decision
mean, <S>.
[0092] 1.1.8 Role of Mathematics in the Integrative Software System
(ISS)
[0093] The role of mathematics in the ISS is important, and is
shown in FIG. 48, for example, where the relation between the ISS
geometry and algebra is shown, as an illustration of parametric
decision process, which is a particular case of an inner network
structure. However, the role of mathematical formalism is also
important in the outer network structure, as discussed in Section
4.0, for example.
[0094] In general, in the case of ISS, the mathematical formalism
does allow both the inner and outer network processes to be more
automated. Although the inner network structure is less automated
than the outer one, it provides a skeleton of how to supervise the
process. For example, in various embodiments, the role of experts
is reduced to an advisory role, rather than a supervisory one.
[0095] 1.1.9 Reduction and Re-Normalization of Unit Vector
Bases
[0096] In the 1.sup.st approximation, the inter-ego and intra-ego
unit vector bases can be considered as mutually orthogonal and
internally orthogonal. In such a case, they can be reduced to
single dimensions, as in FIG. 46, resulting in 2D-space reduction.
Then, both unit vectors, s.sub.i and {circumflex over (k)}.sub.i,
can be analyzed in the 2D space, for sake of simplicity. For the
sake of generality, however, we may consider different
dimensionalities, n.sub.x, and n.sub.y of inter-ego and intra-ego
unit vector bases related, in FIG. 46, to x-coordinate and
y-coordinate, respectively. Because, typically, n.sub.x>n.sub.y,
the scale of inter-ego unit vector basis, Z.sub.x, should be
smaller than the scale of intra-ego unit vector basis,
Z.sub.y:Z.sub.x<Z.sub.y; thus, satisfying the following
relation: Z.sub.x {square root over (n.sub.x)}=Z.sub.y {square root
over (n.sub.y)}. For example, for n.sub.x=6, and n.sub.y=3, we
obtain: Z.sub.y/Z.sub.x= {square root over (6/3)}= {square root
over (2)}=1.414.apprxeq.=1.4 (it should be rather approximated to
lower value). Then it can be assumed that Z.sub.y=14 and
Z.sub.x=10, for example. An example of the re-normalization
procedure is as follows. First, we use: 1=10 scale for both bases,
and then we re-normalize both scales, according to a given
Z.sub.y/Z.sub.x-ratio, resulting in such exemplary numbers as those
used in FIG. 46.
[0097] 1.1.10 Radicalization Level as Decision Parameter
[0098] A parametric decision space such as a Parametric
Radicalization Level (PRL), defining ensemble with parameter
values, S.sub.i, can be a good example of how to narrow the context
while preserving generality. Consider a young population of some
country (state) as an inner network, represented by individuals and
Groups of Interest (Influence). By experiment, find relevant kernel
components can be found: I.sub.i, and T.sub.ij. The process can
then formulate a non-diagonal vector, {right arrow over (H.sub.i)},
including pseudo-vector {right arrow over (G.sub.i)} and intensity
vector I.sub.i. Then, by applying a construction as in FIG. 48, we
can find the PRL response in the form of a weighted average
<S>.
[0099] 1.1.11 Comparison Summary
[0100] In Table 1, a comparison of ISS outer and inner network
structures is presented. Table 1 summarizes the analysis provided
in this Section.
TABLE-US-00002 TABLE 1 Comparison of ISS Outer and Inner Network
Structures No. Feature Outer Inner 1. Correlation Partial Strong 2.
Cost Function Yes Yes 3. Generality More Specific More General 4.
Automation High Medium 5. Basic Mathematics Bayesian Inference
Vector Algebra 6. Network Relation Inter-Network Intra-Network 7.
Basic FoM Bayesian PPV <S>-Accuracy 8. Experts' Minor
Advisory Involvement 9. Software Structure Two engines and
Algorithm several algorithms 10. Basic Methodology Anomalous Events
Moral Skew Factor
[0101] Referring now to Table 1 the correlation (No. 1) is
predominant in the inner network structure, mostly through a
coherency matrix. In contrast, in the outer case, the correlation
is dominant only within the inter-cloud (graphic) engine. In both
cases, cost functions (No. 2) may be applied for system metrics
purposes. The inner network structure may also be more general (No.
3) since it may be applied not only to adverse (hostile) networks
but also to general social networks. On the other hand, the
automation (No. 4) is higher in outer case, and, in parallel, the
experts' involvement (No. 8) is lower, in the outer case. The basic
mathematics (No. 5) of the outer structure are based on Bayesian
inference (Section 4), while, in the inner structure case, the
vector algebra is a basic mathematical tool. Of course, the network
relation (No. 6) is inter-network, and intra-network for outer and
inner cases, respectively, while the basic FoM (Figure of Merit) is
Bayesian Positive Predictive Value (PPV) for outer, and prognostic
accuracy of the parametric decision weighted mean, for the inner
network structure (No. 7).
[0102] The software system structure (No. 9) is more complex in the
outer case (two software engines). Finally, the basic methodology
(No. 10) of the outer structure is based on anomalous events
(BAEVENTS) extraction, while, the inner case phenomenology is
mostly based on Moral Skew Effect (MSE), in general, and on Moral
Skew Factor, in particular.
[0103] Section 2: Example ISS Concepts, Components and Architecture
(Outer Network)
[0104] 2.1 ISS Logic Scheme
[0105] FIG. 1 is a diagram illustrating an example logic scheme in
accordance with one embodiment of the technology described herein.
Referring now to FIG. 1, the example ISS Logic Scheme 99 shown
includes input data 100 and two system software engines, an
intra-cloud software engine 101, and an inter-cloud software engine
102. In various embodiments, inter-cloud software engine 102
produces network graphs, or graphitis 112. While the 1.sup.st
engine can be configured to produce yellow alarms 103, the 2.sup.nd
engine can be configured, with the application of one or more
Compound Association Identifiers (CAIs) 104, produce red alarms
105, which, in turn, can produce the output result, 106.
[0106] Various embodiments can include a feedback loop. The
feedback loop can be used, for example, for training purposes.
System output 106 can be fed back via feedback loop 107 in the form
of Bayesian Truthing Feedback, 108. Through interface 109, Bayesian
Truthing Feedback 108 can be connected with population interface
for truthing of priors (targets), and likelihood probabilities,
110; then, feedback loop 107, is closed. The software engine 101
may be supported by a Bayesian Truthing Inference 113.
[0107] 2.2 Graphitis
[0108] FIG. 2, which comprises FIGS. 2A, 2B and 2C, is a diagram
illustrating examples of graphitis in accordance with one
embodiment of the technology described herein. Graphitis are
network graphs, which can be obtained either exclusively by
collecting network nodes and their connections, as shown in FIG.
2A, or inclusively, using event correlation.
[0109] The example graphiti shown in FIG. 2A has a typical graph
structure with nodes: 200, 201, and edges: 202, 203, 204, etc. The
nodes and edges in various embodiments can be used to represent
network elements. For example, nodes can be used to represent
cyberaddresses, or cyberphone numbers, while edges can represent
cyber-connections with a sufficiently large frequency of
communication events, exceeding some assigned threshold value. In
FIG. 2B, an example graphiti with an appendix 205 is presented.
Such an appendix 205 can be used, for example, to represent some
special HVIC (High Value Individual Candidate). In the example
graphiti shown in FIG. 2C, an extra connection 206 between two
graphitis is presented.
[0110] 2.3 System Architecture
[0111] FIG. 3 is a diagram illustrating an example system
architecture in accordance with one embodiment of the technology
described herein. Referring now to FIG. 3, in this example
architecture, the basic feature is Bayesian Inter-Cloud Coherency
resulting from the integration of two graphitis 220, 221 with
PRO-CLOUDS 222, 223, and 224. A typical number of PRO-CLOUDS is
10-20, while the number of graphitis can be very large, approaching
a million, or more, although other quantities of PRO-CLOUDS and
graphitis can be accommodated in various embodiments. In the
example of FIG. 3, only 2 graphitis are presented for the sake of
simplicity.
[0112] In the illustrated example, an exemplary HVIC (High Value
Individual Candidate) 225 is identified with its cyberaddress 226.
The identity between the two can be provided due to a Compound
Association Identifier (CAI), with its connection 228. Therefore,
the CAI, representing correlation connection 228, is separated from
the intra-cloud causation process, in order to avoid contradiction
between correlation and causation. The professional clouds
(PRO-CLOUDS): 222, 223, and 224, represent different possible HVI
(High Value Individual) professions. In the case of an HVI network,
expemplary professions are given in Table 2.
[0113] Table 2 below is an example identification of selected
PRO-CLOUDS. This example assumes 11 IED network member professions,
and 11 corresponding PRO-CLOUDS. In various embodiments, the
intra-cloud software engine can work, in parallel, with all of the
PRO-CLOUDS, at the same time.
TABLE-US-00003 TABLE 2 Example PRO-CLOUDS 1. Financier 2.
Mastermind 3. Bomb Maker 4. Material Furnisher 5. Spiritual Leader
6. IED Emplacer 7. Triggerman 8. Spotter 9. Bodyguard 10.
Intelligence 11. Camera Man (PR) 12. Others
[0114] 2.4 ISS Cyberspace, Truthing (Sample) Space and System
Envelope
[0115] In general, cyberspace is a computer habitat made up of
interdependent network and information technology (IT)
infrastructures, including the Internet, telecommunication
networks, social networks (e.g., facebook), computer systems, as
well as embedded processors and controllers. It has cyberaddresses,
referred to herein at times as cyberphone numbers (CP#). These can
include phone numbers as a simple example, as well as internet
addresses, e-mail addresses, etc. Hyperspace, including physical
space and cyberspace, generally refers to an abstractive space
including geophysical (x, y, z, t) coordinates and
cyber-coordinates (.xi., .eta., . . . ), representing cyberspace.
Cyber-coordinates can include discrete coordinates such as
cyberphone addresses, and cyberphone numbers (CP#).
[0116] In contrast, the (Bayesian) Truthing (Sample) space is a new
abstractive space created for purposes such as system experimental
validation (truthing) and training. In such a space, the HVIC is a
sample unit, while the HVI is a target. Within this space, the
Bayesian Truthing Inference (BTI) is introduced as a novel approach
to Bayesian inference for ISS purposes. The number of sample units,
m, is preferably sufficiently large in order to justify using
statistical principles, including both classical statistics and
Bayesian statistics.
[0117] Classical statistics is based on a null hypothesis typically
applied to normal (Gaussian) distributions. In such classical
statistics, an anomaly is defined by showing that the null
hypothesis occurrence has a very small probability. Bayesian
statistics, on the other hand, is based on conditional
probabilities, and absolute probabilities (prior known events). The
conditional probabilities can be direct (likelihood) and inverse
(Bayesian), the latter including, for example PPV (Positive
Predictive Value), and NPV (Negative Predictive Value). In some
embodiments, Bayesian algebra, or Bayesian statistics, can be
applied for system training and experimental validation (truthing).
Thus, the ISS can have a well-defined metrics envelope (including
Key Performance Parameters (KPPs), or Figures of Merit (FoMs)), as
well as inputs and outputs. The inputs can include HVIC data coming
from pro clouds, while the outputs can include graphical results
(e.g., graphitis), alarms (e.g., yellow/red alarms), and KPP/FoM
statistical summaries as well as metadata.
[0118] Examples of a system chain structure, system modules
(sub-systems) and Bayesian Truthing Inference, as well as system
performance and concepts of operation (CONOPS) are described
below.
[0119] Section 3: Example System Chain Structure (Outer and Inner
Network)
[0120] 3.1 System Chain Structure
[0121] FIG. 4 is a diagram illustrating an example ISS chain
structure in accordance with one embodiment of the technology
described herein. Referring now to FIG. 4, this example structure
includes 17 elemental tasks (modules), or nodes, with all chain
connections implemented as unidirectional connections. Modules are
numbered as: #1, #2, #3, . . . #17. The example chain structure 300
has demarcation A-A line 301 separating intra-cloud area 303 from
inter-cloud (graphiti) area 304. The feedback line 305 unites those
areas in the opposite direction, while closed feedback loop, 306,
operates clockwise. The #15 module 307 has a switch directing
either into final output, end 308, or into feedback loop 309. A
list of these 17 example modules is presented in Table 3, while
exemplary basic ISS chain features are summarized in Table 4.
TABLE-US-00004 TABLE 3 Example Chain Structure Elemental Tasks
(Modules) No. Name of Elemental Task Nearest Neighbors Type of
Module 1 Input Data (Clouds) #2 Data Base 2 Intra-Cloud Software
Engine #3, #4, #5, #6, Engine #17, #1 3 Bayesian Truthing Inference
(BTT) #2, #4 Algorithm 4 PPV Algorithm #2, #7, #3 Algorithm 5
Pre-Structurization (of Clouds) #2 Algorithm (an option) 6
Cyber-Sensor Output #2, #7 Interface 7 Cost Function Minimization
#4, #6, #8, #9 Algorithm 8 HVI Output Data (Yellow Alarm) #7, #10
Display/Interface 9 HVI Intra-Cloud Feedback #17, #7 Truthing
Algorithm 10 Graph Engine (Graphiti Fabrication) #8, #11, #12
Engine 11 Network Synthesizer System (NSS) #10 Software Sub-System
12 Graphiti Display #10, #13 Display/Interface 13 Graphiti
Experimental Verification #12, #14, #15 Truthing Algorithm 14 Human
Interface (Experts), Optional #13 Human/Machine Interface 15 Final
Output Data (Automated or #13, #16, END Display and Switch Semi-)
16 Graphical (Truthing) Feedback #15, #17 Truthing Algorithm 17
Automated (or, Semi-Automated) #2, #16, #9 Algorithm/Data Base
Injection of Priors
TABLE-US-00005 TABLE 4 Example Chain Features Elemental Tasks No
Feature Description Type of Feature Related to 1 Actionable Chain
Actionability All Tasks (Modules) 2 Positive Predictive Value (PPV)
as PPV (FoM) #4 FoM in #4 3 Cost Function in #7 FoM #4 4
Cybersensor Ranking FoM #2 5 Two Engines #2 and #10 Engines #2, #10
6 Six (6) Supportive Modules to #2 Modules #3, #4, #5, #17, #6, #1
7 After #13, Either END or to #16 Switch #16 8 The 2nd Intra-Cloud
Feedback for Feedback #9 HVIs 9 All Edges are Directional
Actionability All Tasks 10 Critical Modules: #2 and #10 Engines #2,
#10 11 Engine #2 is supported by Bayesian Engine #2 #2, #3
Algorithm #3 12 Priors are Added (Automatically) to Database
Interface #17 Increase PPV-Value for Training 13 Priors Include:
Absolute Cybersensor #17 Probabilities and Likelihood Structure
Probabilities (by Experts, or Automatically) 14 Cost Function as
Module of Algorithm #7 Difference Between (PPV)TH and (PPV)EXP
Should Be Minimized Through Truthing Feedback
[0122] 3.2 System Engines and Feedback
[0123] FIG. 4 depicts an exemplary ISS chain structure that
includes two engines: intra-cloud engine #2 303, and inter-cloud
(graphiti) engine #10 304. It also has two feedback paths:
#15->#16->#17 (global), and #7->#9 (intra-cloud). The
intra-cloud engine #2 takes input from a data source, #1. The
intra-cloud engine #2 also interacts with chain components #3 and
#4 that can be, for example, a Bayesian Truthing Interface and a
PVV algorithm, respectively. The intra-cloud engine #2 can also
interact with a pre-structuraization of clouds algorithm #5. The
intra-cloud engine #2 can then pass output #6 to a cost function
minimization algorithm, #7. The cost function minimization
algorithm can then pass the output to the inter-cloud engine #10,
and/or to the HVI intra-cloud feedback #9.
[0124] Still referring to FIG. 4, the inter-cloud engine can be a
graphiti engine #10. The graphiti engine #10 can take HVI output
data #8 from the intra-cloud engine 303. The graphiti engine #10
can interact with a network synthesizer system (NSS) #11 to display
graphical output in a graphiti display #12. The HVI data can then
be analyzed through a truthing algorithm #13 and/or human
interaction #14. Final output data #15 can then be displayed and/or
sent back to the intra-cloud engine through a feedback algorithm or
database #17.
[0125] FIG. 5 depicts an example heuristics (learning process) as
alternative causation, including three (3) elemental task modules:
#9, #16 and #17.
[0126] 3.3 Intra-Cloud Engine Set
[0127] In the example illustrated in FIG. 4, the ISS chain
structure can be analogized to a workstation production line, with
each elemental task (module) equivalent to workstation, which has
an input, a process, and an output. In some instances, however,
modules can form a cluster surrounding a central module, such as
intra-cloud engine #2, for example.
[0128] FIG. 6 is a diagram illustrating an example of intra-cloud
engine #2 in accordance with one embodiment of the technology
described herein. The intra-cloud engine #2 400 has input 401 from
module #1, and produces output 402 to module #6. It has also two
(2) sub-modules 403, and 404, denoted as #2a and #2b. The 1st
sub-module 403 provides HVIC selection, while the 2nd sub-module
404 is a micro-controller producing a Figure of Merit (FoM). In
this example, the FoM is a ranking parameter determining whether
the HVIC is qualified as an HVI, or not. This decision can be hard
(yes/no), or soft (yes/no/maybe). The other modules, such as 405,
401, 406, etc. provide connections to module 400.
[0129] 3.4 HVI Recommendation Process
[0130] The HVI recommendation process in this example is provided
by Bayesian cyber-sensors CS1, CS2, CS3, CS4, denoted as 407, 408,
409, and 410, respectively. In some embodiments, they are defined
in a narrow sense as Bayesian cyber sensors (BCS), only. The
illustrated quantity, four, is exemplary, and other quantities can
be used. In various embodiments, each cyber-sensor applies one or
more specific Objected-Oriented-Rules (OORs), or its derivative,
DOOR, into a given HVIC, within a given PRO-CLOUD. This can be
done, for example, to show an HVIC's anomaly against a regular
(normal) pattern. In this example, each CS 407, 408, 409, and 410,
has a corresponding readout sub-module R1, R2, R3, R4 to produce a
ranking. For example, higher anomalies receive higher ranking, and
vice-versa. Sensor readouts: R1, R2, R3, R4, are denoted by 411,
412, 413, and 414, respectively. In some embodiments, the rankings
can be weighted with a weight, w. The weighting, for example, can
be within a range:
0<w<1 (6)
[0131] By using voting logic, the weighted combination (e.g., sum)
can be produced as a FoM by sub-module 404. This HVI recommendation
process can be repeated with other HVICs, in sequence, or in
parallel, the latter one through parallel branches 415, 416,
etc.
Example 1
[0132] (Cyber-sensor readout anomaly). Consider a financial
PRO-CLOUD as an example. Consider further that the goal in this
example is to determine whether an anomaly exists for a given HVIC
presenting him or herself as a banker. Thus, the ISS can be
configured, for example, to check the HVIC's financial assets. If,
for example, the ISS finds the HVIC's personal assets below a
certain threshold for a given country (e.g., $10,000 in a country
such as Canada, for example), then its readout sub-module (e.g.,
R.sub.2) gives the HVIC a high ranking (i.e., a high anomaly), such
as a "9," in a scale of 0-10. However, if the HVIC's country is a
third world country, for example, R.sub.2's ranking may be much
lower (lower anomaly).
Example 2
[0133] Assume the answer for EXAMPLE 1 cannot be found. Then, in
this follow-on example, the ISS repeats the process with a similar
OOR, or DOOR. If the ISS is not able to find an answer in a
predetermined number of tries (e.g., three sequential trials), this
itself can be flagged as an anomaly, resulting in a high
ranking.
[0134] As these examples illustrate, in various embodiments, the
process can be configured to (1) identify or determine tests or
rules (e.g., OORs or DOORs) associated with validating an HVIC or
determining whether an anomaly exists; (2) execute those rules
(sequentially or in parallel) to determine a result and rank the
result with a range from non-anomoulous to highly anomalous; (3)
weight the rankings where appropriate; and (4) make a
recommendation regarding whether the HVIC should be considered an
HVI based on the rankings (e.g., by summing or otherwise combining
the rankings).
[0135] FIG. 7, which comprises FIGS. 7A and 7B is diagram
illustrating an example HVI recommendation (decision) process in
accordance with one embodiment of the technology described herein.
A soft decision example is presented in chart a) of FIG. 7, and a
hard decision example is presented in chart b). In the illustrated
example, the high FoM value, a weighted sum of a cybersensor's
BAEVENTS (Bayesian Anomalous Events), produces a positive decision
(yes), while a low value produces negative decision (no). Chart a)
of FIG. 7 also illustrates an example of a neutral decision.
[0136] 3.5 Object-Oriented Rules
[0137] The Object-Oriented Rules (OORs) may, in general, be simple
computer mini-programs to produce BAEVENTS within a given
PRO-CLOUD. Therefore, in various embodiments the OORs may be
cloud-specific, or intra-cloud. (However, their daughters, or
derivatives (DOORs) can be also inter-cloud). The OORs may be
developed using an object-oriented computer language such as, for
example, C++, or Java. Table 5 shows example list of OORs, suitable
for an Organized Crime Network as an example of adverse network.
While non-heuristic OORs are generally developed manually, the
heuristic DOORs can be developed semi-automatically, or
automatically.
TABLE-US-00006 TABLE 5 Example List of Object-Oriented Rules
(OORs), for an Organized Crime Network No. Object-Oriented Rule
(OOR) 1 List of Detainees 2 List Who Communicates with Given HVIC 3
List Who the Given Phone Belongs To 4 List of Organization Where
Given HVIC Belongs 5 List Who has Argued with Given HVIC 6 List of
Arguments Between HVIC1 and HVIC2 7 List of All Events Associated
with Given HVIC 8 Search for a Given Keyword 9 List of the
Associations of All People and Events for Plot Automatic Map
Example 3
[0138] Apply OOR 8 for two (2) keywords: "GOOD," and "OO,"
including word record: HELLO (1), GOOD BYE (2), BLOOD (3), GOOD
(4), and GOODMAN (5).
[0139] Considering keyword: "Good," the match is for the following
words: "GOOD BYE" (2), "GOOD" (4), and "GOODMAN" (5).
[0140] Considering keyword: "OO," the match is for four (4) words:
(2), (3), (4), and (5).
[0141] 3.5 Development Method for DOORs
[0142] Consider the development of Daughter Object-Oriented Rules
(DOORs) as a consequence of applying Boolean logic to
Object-Oriented Rules (OORs), the latter developed by software
engineers. In contrast, the DOORs can be developed
semi-automatically, or automatically within intra-cloud or
inter-cloud schemes. The Boolean logic can be developed by using
either set theory, or binary numbers algebra. FIG. 8, is a diagram
illustrating an example in which the logic "AND," and "OR" (union)
logic operations are shown using set theory. Particularly, the
illustration of AND and OR logic operations, using sets A and B, is
presented.
[0143] In the example illustrated in FIG. 8, as a symbol of
AND-operation 3000, and an OR-operation 3004 as a symbol are
presented. The hatched area 3002 in FIG. 8 illustrates the result
of the AND operation, also called a cross-section. The
OR-operation, also called a UNION, is presented as sum of A, B-sets
as the hatched area 3003, minus their cross-section (to avoid
counting the cross-section, 3004, twice).
[0144] The OR-operation can be understood as "A, or B, or both." In
contrast, the XOR-operation is: "A, or B." Both operations: OR and
XOR, are shown in FIG. 9, using the Boolean algebra.
[0145] According to the example of FIG. 9, the logic operations OR
and XOR are identical, except the last row with both sets A, and B,
equal to 1. FIG. 10 is a diagram illustrating the usefulness of the
XOR operation by showing the summation of two integers "3" and "5,"
which yields "8," using regular (modulo-10) algebra. In contrast,
the Boolean algebra is modulo-2 arithmetic. FIG. 10 at a) shows the
exemplary sum using XOR-logic rule for: "3+5=8". FIG. 10 at b), in
order to show various modulo-algebras, illustrates a scheme of
writing the integer "58," using modulo-7 algebra, for example.
[0146] 3.6 DOORs Based on AND-Operation
[0147] Using Table 5 we can select two OORs: OOR 2 and OOR 8, and
apply the AND-operation to them. FIG. 11, is a diagram illustrating
an example of creating a DOOR in accordance with one embodiment of
the technology described herein. This example illustrates the
creation of DOOR 201, for example (the number of each exemplary
DOOR is for discussion purposes only) by applying the AND-operation
for the following contextual example. The OOR 8 produces a list of
people who mentioned the keyword: "kill." Then, by applying the
AND-operation, the DOOR 201 is obtained, which produces the list of
people who communicate with person named: "Assad," while the OOR 8
produces the list of HVICs who communicate with Assad and mentioned
keyword: kill. In FIG. 11, the Cloud 1, 3010, delivers data to OOR
2, 3011, and OOR 8, 3012, in order to produce DOOR 201, 3013, by
applying AND-operation, 3014. As an example, the OOR 2, 3011,
produces list of people who communicate with "Assad", 3015, while
the OOR 8, produces list of HVICs who mentioned keyword "kill",
3016, resulting in producing by DOOR 201 the list of people who
communicate with Assad and mentioned keyword kill, 3017.
[0148] FIG. 12 is a diagram illustrating the example of creating
DOOR 202. In this example, the other DOOR 202, 3030 is produced as
a combination of OOR 8, 3031, and OOR 7, 3032, using data from
Cloud 2, 3031, and based on AND operation 3033. An example is
applied for illustration, based on associative sentences 3034,
3035, and 3036.
[0149] In FIG. 13, part (a), the compound DOOR 302 is produced by
on union, or OR-operation applied for DOOR 201 and DOOR 202.
[0150] In FIG. 13, part (b), an exemplary equipment logic circuit
of FIG. 13A is presented, including also compositions of DOORs 201
and 202, illustrated in FIGS. 11 and 12, with clouds 1 and 2.
According to FIG. 13(b), clouds 1 and 2 create a habitat for two
pairs of OORs, including their context. In particular, CLOUD 1
creates context for the 1st pair (OOR 2 and OOR 8), while CLOUD 2
creates a context for the 2nd pair. Then, the AND operation for
each pair, creates respective DOORs: the 1st OOR pair creates DOOR
201 and the 2nd OOR pair creates DOOR 202 ("201" and "202" numbers
are chosen arbitrarily). Finally, the OR operation creates the DOOR
302. The DOOR operations can be done automatically, or
semi-automatically.
[0151] 3.7 Context-Based Synonymous Object
[0152] The Context-based Synonymous Object, or CONSYN object
concept is a generalization of the OORs (Object-Oriented-Rules),
based on object-oriented computer languages such as, for example,
C++, Java, or C#. These languages have been created as a response
to a practical need: to modify the object attributes, context and
other object elements (defined as object structure), without
modifying the overall object structure.
[0153] In the context of the ISS, the entity may be considered as
an individual (e.g., a person), or a thing actually existing, such
as, for example, HVI, HVIC, event, object, etc. In particular, an
HVI and HVIC may be considered as an object including its context,
with such context attributes as: e.g. location (within: x, y, z,
t-coordinate system); his/her state (e.g., motion, activity,
physical/emotional condition, etc.); reachability (all cyberspace
media may be included); environmental conditions or surroundings
such as geophysical ones, selection/presentation of
cyberinformation, etc.; identification (e.g., various typed of IDs,
such as driver license, biometric, his/her name, cyberaddress,
individual features/physical and/or mental markings, etc.); other
people and objects belonging to the object and its context (e.g.,
relatives, friends, rats, dogs, etc.); personal preferences;
object-specific databases, and other documents belonging to his/her
context.
[0154] All these object attributes together with the object itself
may be used to create a Context-based Synonymous (CONSYN) object
status, being used within the ISS chain structure, especially
including both software engines. They can be organized within a
CONSYN object GUI (Graphical User Interface), together with other
(possibly: COTS/GOTS) GUIs, and PRO-CLOUDS, as shown in FIG.
14.
[0155] In FIG. 14, an example CONSYN sub-system (algorithm) is
illustrated, including an example CONSYN component itself 2000 and
other possible exemplary COTS/GOTS GUIs, 2001, and 2002. All these
GUIs may be supported by various data from various PRO-CLOUDS, such
as, for example, PRO-CLOUDS 2003, 2004, 2005. The supporting
connections such as 2006, 2007, and others, shown in FIG. 14, are
uni-directional, although bi-directional connections may be
used.
[0156] In the illustrated example, only some PRO-CLOUDS are
supporting a given GUI (e.g., all three (3) PRO-CLOUDS support GUI
1, 2008, while only two (2) PRO-CLOUDS 2004, and 2005, support GUI
2, 2001, and GUI 3, 2002). The CONSYN GUI 2008 supports CONSYN
elements: C1, C2, C3, C4. Some of them, such as C1, 2009, can be
one of the context elements, discussed in paragraph [00125],
including C2, 2010; while, other CONSYN elements, 2011, 2012, can
comprise various cybersensors. All these components may be
summarized into CONSYN algorithm 2013, which has bi-directional
connection with GUI 1. Similarly, GUI 2 2001 and GUI 3 2002 in this
example have bi-directional connections 2015 and 2016 with their
algorithms 2017 and 2018. The same can be said for bi-directional
connections between summary CONSYN algorithm 2019 and partition
algorithms such as 2020, 2021, and 2022.
[0157] This example illustrates that the CONSYN object concept may
be a context-centric one, a feature of this technology, which,
itself, has a specific context of the ISS chain structure. The
bi-directionality of some connections in FIG. 14 does not violate
the actionality principle. This is because it is directly related
to the ISS feedbacks which are well-synchronized within the ISS
chain structure (i.e., feedback loops are separated in time of
operation).
[0158] 3.8 Link Analysis (Network Synthesizer System)
[0159] The ISS applies the Network Synthesizer System (NSS), as in
module #11 of the ISS (see FIG. 4), for the graphiti; i.e., graph
obtained from graph engine #10. In FIG. 15, such a graphiti 4000 is
shown, including illustration of Network Synthesizer System (NSS)
structure at the 1st layer of complication (the lowest). The 1st
layer includes a summary description of the graphiti edges, such as
4001, and nodes, such as 4002. The graphiti nodes may be may be
defined by their cyberphone numbers (CP#s). For ease of
explanation, illustrated is the simplest cyberphone number case,
namely, phone numbers in a shorter form (only seven digits), for
simplicity. For example, we use: "555-3081," instead of a full ten
(10) digit number (with area code), such as "320-555-3081," for
example. The edges represent bi-directional phone connections
between a given two nodes, characterized at the 1st layer, by a
number: "5," for example, denoted by 4004.
[0160] This number represents the total number of telephone
conversations per a given interval, such as during one week, for
example. While the 1.sup.st layer may be represented by the
graphiti, 4005, as in FIG. 15, the 2.sup.nd layer may be
represented by a blow-up 4007 of a given connection, such as 4006,
for example. At the 2.sup.nd layer, the phone conversations may be
represented using more detail including, for example, date (such as
number one) with: Feb. 3, 2015--month, day, year of a given
telephone conversation, 14.04--an hour and minute of conversation,
and "8," eight (8) minutes of conversation duration. In the
exemplary blow-up 4007, four such conversations are described,
which agrees with number "4" 4008. The number of minutes
illustrates an example of a conversation duration, without an
asterisk, such as "8" 4009, which shows conversation initiated by
CP# at the arrow direction, 4010. A duration in minutes, such as
"3," with an asterisk, denoted by 4011, may show a conversation
initiated by CP#, 4012; i.e., against arrow direction. In the
illustrated example, all connections have arrows; thus, this
description is well defined.
[0161] FIG. 16 illustrates an example of a 3.sup.rd layer of
description. At the 3.sup.rd layer of description illustrated in
FIG. 16 (the most complex case in this example), the phone call
bursts (PCBs) are described, as BAEVENTs, which may be results of
Temporal Event Correlation (TEC), or Spatial Event Correlation
(SEC), or both, as illustrated in FIG. 18, for TEC case. For the
sake of clarity, we consider three PCB types, in three colors:
yellow, orange, and red, ending with highest anomaly, such as:
YELLOW BURST:TEC;".largecircle." (7a)
ORANGE BURST:SEC;".quadrature." (7b)
RED:BOTH(TEC and SEC);".gradient." (7c)
[0162] In the example of FIG. 16, the burst symbols are shown in
blow-up 4050, with a scale showing the burst in one-day intervals,
for example, illustrated by dates: 4051 and 4052. The 1.sup.st
burst BAEVENT is a red one, 4053, according to Eq. (7c). The
2.sup.nd is yellow, 4054 and the 3.sup.rd is orange, 4055. The
further action is described in Section 3.10 (Clock Anomaly).
[0163] CONOPS.
[0164] The application of specific layers may be regulated by an
ISS feedback system, according to Section 3.9, where a Compound
Association Identifier (CAI) is described. First, it may be useful
to consider a threshold generating occurrence of the connection
(below this threshold, the connection does not exist in
cyberspace). This stage can be considered as a zero-layer, one of
the simplest ones. After the graphiti is defined, in some
embodiments any layer of description can be applied, depending on
the system of OORs applied for a specific situation.
[0165] 3.9 Compound Association Identifier and Identification (ID)
Method
[0166] The Compound association Identifier (CAI) may be developed
for indirect association between a given HVIC and its cyberphone
number (CP#).
Example 4
[0167] Consider as another example an IED network and a PRO-CLOUD
of Bomb Makers as in Table 2, #3. Assume that the HVIC is
identified as an HVI and that a goal is to determine whether he or
she belongs to a specific graphiti. Further assume that the full
list of CP#s, produced by graph engine #10 is available. The
process can be configured to search all other PRO-CLOUDS containing
CP#s lists. This exemplary situation is shown in FIG. 17, where an
example of Compound Association is presented. This example
identifies identity between the HVI found by software engine #2,
and its CP# found by graph engine #10.
[0168] According to the example of FIG. 17, the Compound
Association Identifier (CAI) 499, provides an elementary
association 500 between two list members having the same CP#462 at
Phone Book 501 and Bank List 502. The 2.sup.nd elementary
association 503 may be found between members having the same bank
account "7," namely, at Bank List 502 and at Transaction List 504.
Therefore, the CAI inferences produce the conclusion in block 507
that the HVI's name is Fred, and also that: "Fred buys a pressure
cooker," i.e., that indeed, this HVI is the bomb maker. This is
shown by two arrows 505, 506 leading to the conclusion. Also, by
identifying Fred's graphiti, the system can be configured to search
other possible HVIs communicating through this identified graphiti,
as possible IED network members.
[0169] 3.10 Clock Anomaly
[0170] The graph engine #10 operation can also be performed by
tracing a clock anomaly (CA). Assume for example that an HVIC Makes
a number of calls and that the calls are counted and time-stamped.
In various embodiments, the fact that he/she is making many calls
does not automatically qualify this person as BAEVENT. However, a
burst of telephone calls within a short duration (e.g., within on
day) can be qualified as the BAEVENT. Therefore, a given number of
calls above a predetermined threshold, within a time window can
qualify as a BAEVENT. Likewise a calls/time ratio above a
predetermined threshold may also qualify. In circumstances where
the burst is in a spatial and/or temporal proximity to an HVI-like
event, the likelihood can be increased.
[0171] As an example, the burst threshold can be set as ten (10)
calls per day, for example, and the threshold can be regulated. If
such a phone call burst (PCB) occurs within a time window of a
terrorist-attractive event, it can be qualified as a soft BAEVENT
(e.g., a medium ranking) in this example. This can be referred to
as being the result of Temporal Event Correlation (TEC). If the
phone call burst occurs in the geographic vicinity of some
characteristic event, then, in this example, there is a Spatial
Event Correlation (SEC), resulting in a medium rank, or a soft
BAEVENT. If they both (TEC and SEC) arrive for the same HVIC, then
this can be classified as a high-ranking BAEVENT.
[0172] FIG. 18 is a diagram illustrating an example of a TEC
situation in accordance with one embodiment of the technology
described herein. Referring now to FIG. 18, in this example, the
time Event Correlation (TEC) is shown, by comparing the frequency
of HVI-like events (graph (a)), and frequency of phone calls (graph
(b)). The time scale in this example is in one-day increments 600,
although other time scales can be used. In this example, there are
two HVI-like events, 601, and 602, and one Phone Call Burst (PCB),
603. Since one of the characteristic events 601 occurs only one day
after the PCB 603 occurred, this can be consider in some
implementations as a Temporal Event Correlation, which may result
in a soft (e.g., medium ranking) BAEVENT, for example.
[0173] 3.11 Parametric Decision and Coherent Coupling
[0174] In order to avoid a correlation/causation contradiction,
various embodiments separate causation and correlation methods
within the ISS chain structure, as discussed above in Section 1.0.
In particular, within this separation, HVIs may be organized within
various kinds of social networks, such as terrorist networks, for
example. Accordingly, in various embodiments, dynamic decision
processes can be included, which, for example, can be dependent on
power (intensity) and coherent coupling between HVIs, or other
social network members. Whenever and wherever a decision should be
made, there may be a spectrum of decisions to be considered, where
one of them, (not necessarily the optimal one) will be selected.
This section describes example processes for predicting the
selected decision, using novel modeling based on coherent
coupling.
[0175] In various embodiments, the system can be configured to
consider the expected decision as weighted mean, <S>, where
S-decision, and < . . . > symbolizes the mean average, while
S.sub.i is a decision preferred by ith-member of a social network,
and w.sub.i is his/her weight, normalized to unity. This weight may
be proportional to his/her strength, influence or power (intensity)
within the network.
[0176] In further embodiments, the decision spectrum within the
network for a given decision may be parameterized as a positive
integer set (e.g., S.sub.1, S.sub.2, S.sub.3, . . . , where
S.sub.1<S.sub.2<S.sub.3, . . . ). A decision parameter can
be, for example, a risk factor, a cost factor, etc. The system may
be configured such that a higher risk results in a higher S-value,
and vice versa.
[0177] Coherent coupling may also be used as part of the analysis.
Assume, for example, a quantity of N social network members (e.g.,
i=1, 2, 3, . . . , N) organized in the form of a graph (not
graphiti), where i-nodes denote members and edges denote their
mutual couplings. For example, edge ij represents a coupling
between the ith and jth members. The member's strength, or kernel
K.sub.i, can depend on his/her own strength, influence or
intensity, I.sub.i, and his/her coherent coupling. The coherent
coupling ij-term is proportional to a geometrical mean {square root
over (I.sub.iI.sub.j)} among member intensities, as well as to a
coherency matrix element T.sub.ij. Coherency matrix element
T.sub.ij may be defined as: T.sub.ii=1, and T.sub.ij.ltoreq.1. The
number of such coherent couplings for N-number of members is N
(N-1)/2. For example, for N=5, we obtain 10 coherent
connections.
[0178] However, these connections may be bi-directional, and matrix
element, T.sub.ij, does not need to be equal to T.sub.ji, in
general. In addition, there may also be, N self-couplings.
Therefore, the total number of couplings, may be:
[ N ( N - 1 ) 2 ] ( 2 ) + N = N 2 ( 8 ) ##EQU00002##
[0179] 3.11.1 Mathematical Model
[0180] The decision weighted mean, <S>, is
< S >= i = 1 N S i K i i = 1 N K i ( 9 ) ##EQU00003##
[0181] where ith-weight, is
w i = K i i = 1 N K i ; 0 .ltoreq. w i .ltoreq. 1 , and i = 1 N w i
= 1 ( 10 a ; 10 b ; 10 c ) ##EQU00004##
[0182] The social network members (i=1, 2, . . . N) may be
organized within a graph, as shown in FIG. 19, where edges are
denoted with the symbol ".parallel." to differentiate them from
graphiti edges, as in FIG. 2, for example. In the example
illustrated in FIG. 19, N=6. Therefore, N(N-1)/2=15, and
N.sup.2=36.
[0183] The strength kernel, K.sub.i, may be defined as:
K i = j = 1 N T ij I i I j ( 11 ) ##EQU00005##
[0184] where, for diagonal elements of the coherency matrix,
T.sub.ij, we have:
T.sub.ii=1 (12)
[0185] while all (real, positive) matrix elements satisfy the
inequality:
T.sub.ij.ltoreq.1 (13) [0186] Where the convention used is such
that T.sub.ij means: the ith-member influencing the jth-member, and
T.sub.ji is the reverse.
[0187] FIG. 20 is a diagram illustrating an example of such a
coherency matrix for N=3. In instances where members have identical
strengths:
I.sub.i=I=CONSTANT (14)
[0188] and, Eq. (7) becomes:
K i = I j = 1 N T ij ( 15 ) ##EQU00006##
[0189] and, the weight, is
w i = i = 1 N T ij i = 1 N j = 1 N T ij ( 16 ) ##EQU00007##
[0190] In other words, the weight depends only on the coherency
matrix elements. This represents a crowd-like environment, where N
is a large number. In the case where all coupling elements are
equal:
T.sub.ij=T=const (17)
[0191] And the weight simply becomes
w i = 1 N ( 18 ) ##EQU00008##
[0192] However, this formula is valid only for very strong
couplings, since: T.sub.ii=1.
[0193] Normal Parametric Order.
[0194] For purposes of discussion, consider a natural assumption
that the coupling is the strongest between members with close
parameters. This can be accomplished, for example, by applying a
Normal Parametric Order (NPO). FIG. 21 is a diagram illustrating an
example of applying an NPO in the case of N=3. Referring now to
FIG. 21, in such a case, a monotonic parameterization can be
assumed in which:
S.sub.1<S.sub.2<S.sub.3 (19)
[0195] as shown in FIG. 21.
[0196] FIG. 22 illustrates an example of a normal parametric order.
In the example illustrated in FIG. 22, only three members are
considered (i=1, 2, 3), and each member has monotonic preferable
decision, as in Eq. (19). This scheme may be generalized to cases
in which N>3. In such a case for the NPO, we can introduce a new
k-index, in the form:
k=i-j (20)
[0197] Thus, the NPO represents space-invariant case, in the
form:
T.sub.ij=T.sub.i-j=T.sub.k (21)
[0198] Now, the NPO can be defined as the system with the following
basic properties for the coherency matrix elements (as shown in
FIG. 22):
a) Space invariant (22a)
b) Symmetrical (22b)
c) Monotonic (22c)
[0199] In FIG. 22, three (3) basic properties of the Normal
Parametric Order (NPO) are illustrated, including:
space-invariance; symmetry; and monotonic. The NPO is space
invariant because according to Eq. 17, the coherency matrix
element, T.sub.k, depends only on one index, k, where, for i=j, we
have: T.sub.ii=T.sub.o=1.
[0200] Also, the NPO is symmetrical (please, see, Eq. 22(b))
because:
T.sub.k=T.sub.-k (23)
[0201] The NPO is also monotonic (22c), or constantly decreasing.
In contrast, the abnormal or anomalous distribution will violate
one or more of those properties. As an example of the NPO
distribution, consider another case in which N=3 as illustrated in
FIG. 23. In FIG. 23, the space-invariant coherency matrix elements,
are:
T.sub.0=1; T.sub.1=T.sub.-1=0.5; T.sub.2=T.sub.-2=0
(24a;24b;24c)
[0202] In FIG. 24, the related coherency matrix is shown.
[0203] For illustration, we consider two examples, one satisfying
Eqs. (24a; 24b; and 24c) and the other one not satisfying this
relation. In both cases, the following parametric decision
parameter values apply:
S.sub.1=1; S.sub.2=5; S.sub.3=10 (25a;25b;25c)
[0204] In the 1.sup.st case, the kernel values are:
K.sub.1=T.sub.11I.sub.1+T.sub.12 {square root over
(I.sub.1I.sub.2)}+T.sub.13 {square root over
(I.sub.1I.sub.3)}=(1)I+(0.5)I+(0)I=1.5I (26)
K.sub.2=T.sub.21 {square root over
(I.sub.2I.sub.1)}+T.sub.22I.sub.2+T.sub.23 {square root over
(I.sub.2I.sub.3)}=(0.5)I+(1)I+(0.5)I=2I (27)
K.sub.3=T.sub.31 {square root over (I.sub.3I.sub.1)}+T.sub.32
{square root over
(I.sub.3I.sub.2)}+T.sub.33I.sub.3=(0)I+(0.5)I+(1)I=1.5I (28)
[0205] Thus, the kernel sum, is
K.sub.1+K.sub.2+K.sub.3=1.5I+2I+1.5I=5I (29)
[0206] and, the weights, are:
w.sub.1=1.5/5=0.3; w.sub.2=2/5=0.4; w.sub.3=1.5/5=0.3
(30a;30b;30c)
[0207] Therefore, the weighted (decision) mean, is
<S>=(1)(0.3)+5(0.4)+10(0.3)=0.3+2+3=5.3 (31)
[0208] In the 2.sup.nd case, we assume that Eq. (14) is not
satisfied. Instead, we assume:
I.sub.1=4I.sub.o; I.sub.2=I.sub.o; I.sub.3=I.sub.o
(32a;32b;32c)
Then, we have:
K.sub.1=(1)4I.sub.o+(0.5) {square root over (4I.sub.oI.sub.o)}+(0)
{square root over (4I.sub.oI.sub.o)}=4I.sub.o+1I.sub.o+0=5I.sub.o
(33)
K.sub.2=(0.5)(2I.sub.o)+(1)(I.sub.o)+(0.5)(I.sub.o)=2.5I.sub.o
(34)
K.sub.3=(0)I.sub.o+(0.5)I.sub.o+(1)I.sub.o=1.5I.sub.o (35)
and,
K.sub.1+K.sub.2+K.sub.3=5I.sub.o+2.5I.sub.o+1.5I.sub.o=9I.sub.o
(36)
and, the weights, are
w.sub.1=5/9=0.55; w.sub.2=2.5/9=0.28; w.sub.3==1.5/9=0.17 (37)
[0209] As a check, the following relation can be examined:
w.sub.1+w.sub.2+w.sub.3=55+0.28+0.17=1 (38)
[0210] Thus, the mean decision, is
<S>=1(0.55)+5(0.28)+10(0.17)=3.61 (39) [0211] i.e., smaller
than that from Eq. (30), where: <S>=5.3. We see that higher
strength (intensity) of I.sub.1=4I.sub.0 (vs. I.sub.1=I.sub.o),
created more attraction into decision, S.sub.1 (since, S.sub.1=1),
as it is expected.
[0212] 3.11.2 Anomalous Coupling
[0213] Any deviations from the Normal Parametric Order, we classify
as Anomalous Coherent Coupling (ACC). Such deviations may be
presented in the series form:
T.sub.ij=T.sub.ij.sup.(0)+T.sub.ij.sup.(1)+T.sub.ij.sup.(2)+ . . .
(40) [0214] where the zero.sup.th term, T.sub.ij.sup.(0), is
related to the NPO and the subsequent terms relate to the anomalous
order. They usually are of the 1.sup.st order, or higher-order
small quantities, but they may sometimes be comparable with the
zero-order term. These deviations can violate any of the properties
(equations 19a, 19b 19c) of the NPO, or a combination of
thereof.
[0215] 3.11.3 Dynamic Coupling
[0216] In addition to the anomalies, the coherent coupling can be a
dynamic coupling. In some embodiments, it can be in the form:
T.sub.ij=T.sub.ij(t) (41) [0217] where t is time. This dynamic
coupling can be obtained from some intelligence data, such as data
related to personal relations, or any other mutual relations, but
typically not from the typical relation of closer opinion=stronger
coupling. (It should be noted that the individual strength has
already been included in the form of intensities).
[0218] For prediction purposes, the process may typically begin
with the normal form, and then introduce deviations according to
Eq. (40). Then, the weighted mean, <S>, will be evaluated as
a function of time; leading to a new or refined conclusion. The
coherency matrix (and intensity) can also be changed by design in
order to model or evaluate what would happen if conditions were to
change.
[0219] 3.11.4 Inter-Group Coupling
[0220] Group interaction can have a similar form to an interaction
between individuals. However, in some embodiments, group kernels
are introduced as more global figures. These can be in the
form:
K.sub.m; m=1,2,3, . . . M (42) [0221] where M is the number of
groups. The modeling can be similar, but preferably, group kernels
are located and identified.
[0222] FIG. 25 is a diagram illustrating an example of identifying
group kernels in accordance with one embodiment of the technology
described herein. In FIG. 25, two exemplary groups 1000 and 1001
are presented in the form of graphs (not graphitis). The nodes,
such as 1002, and 1003, for example, represent individuals, while
edges, such as 1004, 1005, 1006, for example, represent coherent
couplings between nodes. The connection 1007 represents group
coupling outside of group boundaries 1008 and 1009 defining a group
territory. After finding group kernels, the system applies a
generalization of formula (5), which can be in the form:
S = m = 1 M S m K m m = 1 M K m ( 43 ) ##EQU00009##
where M is the number of groups, and m is a group index. The system
can be configured to also apply other formulas (e.g., 6-7), in an
analogous fashion.
[0223] Section 4: Bayesian Truthing Inference (Outer Network)
[0224] 4.1 Bayesian Inference and Binary Sensors
[0225] The experimental validation (truthing) used by the systems
and methods described herein is, in some embodiments, based on a
Bayesian Truthing Inference (BTI). The BTI is a novel concept
derived from Bayesian inference and Binary Sensors formalism.
Following signal theory, consider two exclusive events: a signal
(target) event, denoted by the capital letter 5; and a no-target
event (noise), denoted as N, with so-called prior absolute
probabilities, p(S) and p(N), respectively. These can be configured
to satisfy the conservation relation:
p(S)+p(N)=1 (44)
[0226] The binary event (S, N) is detected by binary sensor, with
two exclusive readings. For example two readings can be an alarm
(5') and no alarm (N'). Their probabilities can satisfy the
conservation relation:
p(S')+p(N')=1 (45)
[0227] In the ISS case, the binary sensor decision may be made by
sub-module #2b 404, as shown in FIG. 6. For example, this can be
done by producing an alarm (e.g., a yellow alarm) sent into Module
#6 402, informing Module #6 402 that a given HVIC has been
qualified as HVI. A no alarm event can be determined to mean that
the given HVIC has not been qualified as HVI. Therefore, a hard
decision is made by sensor 404, and this is a binary decision
(while a soft decision can be referred to as omniary--i.e., it can
have more than 2 states).
[0228] Likelihood Probabilities.
[0229] The likelihood probabilities are (direct) conditional
probabilities about the probability of the binary decisions S' or
N', assuming that the binary event occurred. It is noted that
symbols "S" should not be confused with the parametric decision
symbol.
p(S'|S)--probability of detection (POD) (46a)
p(N'|N)--probability of rejection (POR) (46b)
p(S'|N)--probability of false positives (PFP) (46c)
p(N'|S)--probability of false negatives (PFN) (46d)
[0230] They satisfy the following conservation relations:
p(S'|S)+p(N'|S)=1 (47)
p(S'|N)+p(N'|N)=1 (48) [0231] The name "false positive," for
example, may be chosen because a positive reading (5') is false in
circumstances where no target event (N) actually occurred.
[0232] FIG. 26 is an example of a Bayesian Inference causality
diagram in accordance with one embodiment of the technology
described herein. In the example of FIG. 26, a Bayesian Inference
causality diagram 699 is shown for binary sensors. This example
illustrates two events (S, N) as causes 700 and 701, and two sensor
readouts 702 and 703 as effects. In the illustrated example, this
causation relation is well defined, because the causation relations
704, 705, 706, and 707 are unidirectional, while both causes 700
and 701 and effects 702 and 703 are mutually exclusive. Also shown
by this example is that diagram 699 represents a probability
(Bayesian) network, with the conservation Eq. (44), denoted by 708,
and the conservation Eq. (45), 709. Also, the causation connection
704 represents probability of detection p(S'|S) (Eq. (46c)), while
the probability of false negatives p(N'|S) (Eq. (46d)), for
example, is represented by connection 705.
[0233] 4.2 Positive Predictive Value and Bayesian Paradox
[0234] Using Bayes theorem, inverse conditional probabilities such
as p(S|S'), p(N|N'), p(N|S'), and p(S|N') can also be considered
and utilized. Probabilities p(S|S') p(N|N') may be important for
the evaluation, including that of the Positive Predictive Value
(PPV). The Positive Predictive Value can be in the form:
(PPV)=p(S|S') (49)
[0235] and Negative Predictive Value (NPV), in the form:
(NPV)=p(N|N') (50)
[0236] Using Bayes theorem for binary sensors the following
relation for (PPV) FOM can be derived:
( PPV ) = p ( S S ' ) = 1 1 + q 1 where ( 51 ) q 1 = p ( S ' N ) p
( N ) p ( S ' S ) p ( S ) ( 52 ) ##EQU00010##
[0237] Because the target events are usually rare, we can
write:
p(S)<<1 (53)
[0238] thus, p(N).apprxeq.1. Also, false negatives are usually low:
p(N'|S)<<1; thus,
p(S'|S).apprxeq.1 (54)
[0239] and Eq. (10) reduces to the following form:
( PPV ) = p ( S S ' ) = 1 1 + p ( S ' N ) p ( S ) ( 55 )
##EQU00011##
[0240] This formula may be referred to as the Bayesian Paradox,
because, in spite of high value of Probability of Detection, as in
Eq. (54), the PPV-critical figure can be low, especially for a low
prior (target) population, as in Eq. (53). FIG. 27, illustrates an
example Bayesian Paradox. According to FIG. 27, the following
relation is satisfied:
p ( S ' N ) p ( S ) > 1 ( PPV ) < 0.5 ( 56 ) ##EQU00012##
i.e., if the prior probability, p(S), is smaller than the
probability of false positives, p(S'|N), then, the (PPV) is smaller
than 50%. Thus, in order to obtain high (PPV)-values, the system
can be configured to produce a relatively high prior population. In
some embodiments, this is much higher than likelihood probability
of false positives:
p(S'|N)<<p(S)(PPV).apprxeq.1 (57)
In contrast to the PPV, the NPV-figure is typically always close to
100%, in practice.
[0241] 4.3 Bayesian Truthing
[0242] 4.3.1 Truthing Sampling Space
[0243] The Truthing Sampling Space (TSS) is discrete and can be
quantized by sample units (such as HVICs, for example) in which the
number of samples, m, may be very large:
m>>1 (58)
[0244] Nine exemplary truthing parameters can be considered in
various embodiments. For purposes of discussion, these example
parameters are defined by lower case letters as listed below.
m--number of samples (59a)
s--number of targets(signals) (59b)
n--number of no-targets(noises) (59c)
a--number of alarms (59d)
a.sub.1--number of true alarms (59e)
a.sub.2--number of false alarms (56f)
b--number of no-alarms (59g)
b.sub.1--number of true no-alarms (59h)
b.sub.2--number of false no-alarms (59i)
[0245] Using these parameters, Bayesian probabilities, such as a
prior (target) probability, for example, can be defined:
p ( S ) = lim m -> .infin. s m ( 60 ) ##EQU00013##
[0246] Based on this method, the previous statistical relations can
be derived using truthing parameters such as:
n+s=m (61a)
a+b=m (61b)
a=a.sub.1+a.sub.2 (61c)
b=b.sub.1+b.sub.2 (61d)
a.sub.1+b.sub.2=s (61e)
b.sub.1+a.sub.2=n (61f)
[0247] Among these six (6) example statistical relations, five (5)
of them are independent, while the total number of truthing
parameters is nine (9):
m,s,n,a,a.sub.1,a.sub.2,b,b.sub.1,b.sub.2 (62)
Therefore, four (4) parameters are free, while the remaining five
(5) can be found by solving the five (5) independent Eqs.
(61a,b,c,d,e & f).
[0248] In FIG. 28, examples of Bayesian Truthing Sets are
illustrated, including a non-ideal system (a) and an ideal system
(b). The example target set 800 is north/east-south/west shaded;
while the alarm set 801, is north/west-south/east shaded. A
no-target & no-alarm set 802 represents true no-alarms.
Therefore, the crosshatched set 804 represents true alarms
(a.sub.1). On the other hand, the no-alarm set, 803, represents
true no-alarms (b.sub.1). Then, the set 805 is the target set which
is not alarmed; i.e., false no-alarms (b.sub.2), while the set 806
is the noise set, which is alarmed (i.e., false alarms
(a.sub.2)).
[0249] In FIG. 28 with the ideal system b), however, there are no
single-hatched sets (a.sub.2=b.sub.2=0); thus, representing the
ideal system. Also, using FIG. 28 for the non-ideal system a), the
conservation relations (58e) and (58f) can be identified. For
example, symbolically this can be written as
"804"+"805"="800" (63)
which is equivalent to Eq. (61c), because symbolically:
a.sub.1="804," b.sub.2="805," s="800" (64a;64b;64c)
[0250] 4.4 Bayesian Truthing Theorem (BTT)
[0251] The Bayesian Truthing Theorem (BTT) can be easily derived,
using the truthing parameters in Eq. (62). Using parameters from
Eq. (62), the likelihood probabilities can be rewritten in the
form:
p ( S ' S ) = a 1 s ( 65 a ) p ( N ' S ) = b 2 s ( 65 b ) p ( S ' N
) = a 2 n ( 65 c ) p ( N ' N ) = b 1 n ( 65 d ) ##EQU00014##
Substituting these into Eq. (52) yields:
q 1 = p ( S ' N ) p ( N ) p ( S ' S ) p ( S ) = ( a 2 n ) ( n m ) (
a 1 s ) ( s m ) = a 2 a 1 ( 66 ) ##EQU00015##
Therefore, the PPV-para meter, is
( PPV ) = 1 1 + q 1 = 1 1 + a 2 a 1 = a 1 a ( 67 ) ##EQU00016##
which is the Bayesian Truthing Theorem (BTT), the basic Bayesian
formula for the ISS evaluation. It can be written as:
( PPV ) = p ( S S ' ) = NUMBER OF TRUE ALARMS TOTAL NUMBER OF
ALARMS ( 68 ) ##EQU00017##
It should be noted that this formula can be used without knowledge
of the Bayesian inference; because the number of alarms, true and
false, can be directly found from experimentation.
[0252] In a similar way, the NPV-figure can be derived, as
( NPV ) = b 1 b = NUMBER OF TRUE NO - ALARMS TOTAL NUMBER OF NO -
ALARMS ( 69 ) ##EQU00018##
Where NPV is the Negative Predictive Value.
[0253] 4.5 Analogy Between X-Ray Luggage Inspection and the ISS
[0254] The Binary Sensor concept has broad applicability, and it
can be used in applications such as, for example, ATR (Automatic
Target Recognition); QC (Product Inspection); Homeland Security
(X-Ray Luggage Inspection against Explosives); Legal (Judicial
Verdict); Medicine (X-Ray Breast Cancer Diagnosis); Software (ISS);
to name a few. In any case, the target is typically some anomalous
sample such as, for example, Luggage with Explosives, a Positive
Cancer Diagnosis, a Defective Product, HVI, etc. The case of x-ray
luggage inspection at airport terminals is perhaps the easiest case
to explain, and will be used herein by way of example. Therefore,
Table 6 presents a comparison between the x-ray luggage inspection
and the ISS.
TABLE-US-00007 TABLE 6 Comparison of Statistical and
Truthing*.sup.) Parameters for X-Ray Luggage Inspection and
Integrative Software System (ISS) Integrative X-Ray Luggage
Software System No Parameter Name Symbol Inspection (ISS) 1 Sample
(Number) m One Luggage HVIC** 2 Target S Luggage with HVI***
Explosives 3 Noise (No Target) N Luggage with No Non-Adverse
Explosives Person 4 Target (Number) s Targets' Number Targets'
Number 5 Alarm S' System Alarm System Alarm 6 True/False Alarm
a.sub.1/a.sub.2 True/False Alarms' True/False (Number) Number
Alarms' Number *.sup.)"Truthing" name is introduced by analogy to
radar truthing, where target/clutter mockups/natural objects have
been tested at the ground by airborne radar.
**High-value-individual "candidate." ***High-value-individual (IED
network member, for example).
[0255] 4.6 Numerical Examples Illustrating ISS Bayesian
Truthing
[0256] For explanation by way of example of an ISS Bayesian
Truthing, consider a number of numerical examples illustrating
orders of magnitude of basic truthing parameters, by applying
(arbitrarily) four (4) free parameters.
Example 5
[0257] Consider a sample size m=10.sup.7 (large sample);
p(S)=10.sup.-6 (rare events); p(S'|N)=10.sup.-5; p(N'|S)=10.sup.-3.
In this example,
p ( S ) = s m s = mp ( s ) = ( 10 7 ) ( 10 - 6 ) = 10 and ( 70 ) p
( N ' S ) = b 2 s b 2 = sp ( N ' S ) = ( 10 ) ( 10 - 3 ) = 10 - 2 (
71 ) ##EQU00019## [0258] Eq. (71) shows, that, in spite of
relatively large false negatives (10.sup.-3), target misses almost
never occur (b.sub.2<<1).
[0259] Furthermore:
n=m-s=10.sup.7-10=9999990 (72)
and,
P(S'|N)=10.sup.-5a.sub.2=np(S'|N)=(9999990)(10.sup.-5).apprxeq.100
(73)
and,
b.sub.1=n-a.sub.2=9999990-100=9999890 (74)
thus,
b=b.sub.1+b.sub.2=9999890+10.sup.-2=b.sub.1 (75)
[0260] Therefore, because b.sub.2<<1, then,
b.apprxeq.b.sub.1, and, indeed the Negative Predictive Value is as
follows
(NPV).apprxeq.1 (76)
[0261] In order to find the PPV-figure, however, we need to find
the numbers of true alarms, a.sub.1, and total number of alarms, a,
in the form:
a=m-b=10.sup.7-9999890=110 (77)
while,
a.sub.1=a-a.sub.2=110-100=10 (78)
[0262] thus, the PPV-figure is low:
( PPV ) = a 1 a = 10 110 = 0.09 = 9 % ( 79 ) ##EQU00020##
[0263] In fact, this value could be anticipated by applying the
Bayesian Paradox formula with an approximate q.sub.1-value, which
can (directly) be found from the input data:
q 1 = p ( S ' | N ) p ( S ) = 10 - 5 10 - 6 = 10 ( 80 )
##EQU00021##
[0264] so, approximately, the PPV-value, is
( PPV ) = 1 1 + q 1 = .about. 1 1 + 10 = 0.09 ( 81 )
##EQU00022##
[0265] which coincides with Eq. (67).
[0266] For further checking, the conservation formula yields:
a+b=110+9999890=10.sup.7 (82)
Example 6
[0267] Assume m=10.sup.7, s=10, a.sub.2=b.sub.2=10.sup.-2. This
time, we are applying only truthing parameters. Thus, calculation
of the Bayesian figures: PPV and NPV is much simpler; because,
a.apprxeq.a.sub.1; h.apprxeq.b.sub.1 (83a; 83b)
thus,
(PPV)=(NPV).apprxeq.1 (84) [0268] and the system is close to ideal
one (almost no false negatives and no false positives).
[0269] 4.7 Relations Between Non-Diagonal Statistical and Truthing
Parameters
[0270] The non-diagonal Bayesian statistical parameters are
probabilities of false positives and false negatives. By analogy,
the non-diagonal Bayesian truthing parameters can be defined as the
Probability of a False Alarm (PFA) and the Probability of a False
no-Alarm (PFnA), in the form:
( PFA ) = a 2 m ( 85 a ) and ( PFnA ) = b 2 m ( 85 b )
##EQU00023##
[0271] Then:
b 2 = m ( n m ) ( b 2 s ) = mp ( N ) p ( N ' | S ) ( 86 ) and , a 2
= m ( n m ) ( a 2 n ) = mp ( N ) p ( S ' | N ) ( 87 )
##EQU00024##
[0272] Therefore, the following relations between non-diagonal
truthing and statistical parameters can be derived:
( PFA ) = a 2 m = p ( N ) p ( S ' | N ) ( 88 ) ( PFnA ) = b 2 m = p
( S ) p ( N ' | S ) ( 89 ) ##EQU00025##
[0273] These relations are non-singular, because, for statistical
purposes, the prior probability can neither equal 1 nor 0:
0<p(S)<1 (90) [0274] Therefore, the ideal system, with both
zero false negatives and zero false positives, is possible, by
satisfying the relations
[0274] (PFA)=(PFnA)=p(S'|N)=p(N'|S)=0 (91)
[0275] Also, because targets are usually rare events:
P(S)<<1p(N).apprxeq.1 (92)
[0276] thus, according to Eq. (88), we obtain:
(PFA).apprxeq.p(S'|N) (93) [0277] i.e., the Probability of False
Alarm (PFA) is (almost) equal to Probability of False Positives
(PFP).
[0278] However, according to Eq. (89), the Probability of False
no-Alarm, PFnA, is much smaller than the Probability of False
Negatives (PFN):
(PFnA)<<p(N'|S) (94)
[0279] This is why in Example 5, the result is b.sub.2<<1, in
spite of the fact that the PFN is rather high (10.sup.-3).
[0280] 4.8 Lossless Multi-Alarm Method
[0281] In spite of the fact that the ideal system can be realized
theoretically as in Eq. (88), practically, there is a trade-off
between false positives and false negatives. Therefore, very often,
the target misses are low, while the PFA is high. Therefore, in
various embodiments, a multi-step (multi-alarm) cascade Lossless
Multi-Alarm (LMA) method can be applied. Thus, assuming:
b 1 = .about. b ( 95 ) with , ( PPV ) = a 1 a << 1 ( 96 )
##EQU00026##
the LMA method can be applied.
[0282] FIG. 29 is a diagram illustrating an example methodology of
an LMA method. This example includes two (2) sampling spaces 900
and 901. Assuming Eqs. (95-96) are satisfied, the 1.sup.st alarm,
902, is produced with (almost) zero false negatives (b.sub.2<1),
but high false positives ((PPV)<<1). Then, the 2.sup.nd
sampling space 901 does not have (almost) target misses; i.e., the
whole target (prior) population is preserved. Then, the 2.sup.nd
alarm 903 is produced, in order to reduce false positives. This
results in the output 904 as a high (PPV)-value. Therefore, a
two-sensor method, including Sensor 1 905 and Sensor 2 906 is
better than a single-sensor method, if we are able to differentiate
sensor technology into two sensor subsystems.
[0283] Such a situation may be realized in medical diagnostics, for
example, based on x-ray breast cancer inspection (Sensor 1, 905).
In order to avoid a biopsy in the second step, the patients with a
positive cancer diagnosis after Sensor 1 (satisfying conditions
95-96) are sent to some other specialized diagnosis shown by Sensor
2, 906. This diagnosis can be, for example, ultrasound. Then,
patients with output 904 satisfying a high PPV-value are finally
sent to the biopsy.
[0284] Section 5: System Performance Components (Outer Network)
[0285] This section discusses some exemplary critical performance
components for effective performance of the ISS (some of which have
already been discussed in previous sections).
[0286] 5.1 Cost Function
[0287] The training of an Integrative Software System may be
provided with the help of a cost function, CF, defined as:
(CF)=|(PPV).sub.TH-(PPV).sub.EXP| (97)
where | . . . | is a modulus (absolute value) operation. The
(PPV).sub.TH is based on a Bayesian Paradox formula (in the
simplest case, equal to this formula). This parameter can be
obtained only with help of Bayesian inference, including a
statistical parameter, such as a PFP. It may be obtained either
automatically as linear regression from training data, or
semi-automatically with help of expert queries. Therefore,
theoretically, this parameter is based on prior absolute and
likelihood probabilities. It depends on prior population, p(S), and
system performance, defined mostly by p(S'|N)-(PFP) value.
Increased training in the target population also increases the
(PPV).sub.TH parameter. Then, for a constant prior population
influx, the (PPV).sub.TH parameter remains constant, or varies
slowly. In contrast, the (PPV).sub.EXP parameter may be strongly
fluctuating. In some embodiments, the system is configured to
increase its value by training (it can be defined as ratio of red
alarms to yellow alarms), until it stabilizes, as shown in FIG.
30.
[0288] In FIG. 30 at chart a), both (PPV)-parameters are shown,
including (PPV).sub.EXP-parameter, 1000, and (PPV).sub.TH, 1001,
with the nodes 1002, 1003, etc., defining a crossing of these two
functions during a training process. This is characterized by time
the scale t' denoted as 1004. These nodes, 1002 and 1003, for
example, correspond to (CF) function's 1007 zero values 1005 and
1006, respectively. This illustrates that the CF-function
fluctuates with fluctuations decreasing as time t' increases. In
the case of well-performed training, these fluctuations decrease
asymptotically to zero, as shown by part of CF-curve 1008 (chart
b)).
[0289] The introduction of a (PPV).sub.TH support function (during
the ISS training) is analogous to applying mockup prey as an
attraction to dogs in the initial stage of a dog race.
[0290] 5.2 System Feedback
[0291] At least two (2) feedback mechanisms are introduced in FIG.
4. The 1.sup.st one is a local feedback path and includes a switch
at module #7, which performs a cost function minimization. This
feedback can be configured to regulate and minimize cost function
fluctuations, as in FIG. 30. This can be achieved, for example, by
regulating (increasing/decreasing) prior population and system
performance (e.g., by adding mockups, or natural objects).
[0292] The 2.sup.nd feedback in this example is global feedback
(#15, #16, #17, #2), which maximizes global (PPV) as a ratio of red
alarms to yellow alarms, by regulating (PPV).sub.EXP function. This
can be accomplished, for example, in the following form (the other
form derivatives are also possible; this one is the simplest
one):
( PPV ) EXP = NUMBER OF RED ALARMS TOTAL NUMBER OF YELLOW ALARMS (
98 ) ##EQU00027##
[0293] This feedback can be configured in some embodiments to
minimize fluctuations of the (CF) function, as shown in FIG.
30.
[0294] 5.3 Dual Engine Connection
[0295] Two basic system engines #2 and #10, as illustrated in the
example of FIG. 4, can be configured to work in parallel, producing
independent results. This can be done, for example, in order to
maximize the system performance quality and efficiency. The
intra-cloud engine #2 produces HVIs, which may be selected from
HVICs, as yellow alarms. The inter-cloud engine #10 can be
configured to produce graphitis, with CP# as graphiti nodes. One
goal in various embodiments is to identify a maximum number of the
HVIs with CP#, in order to produce real alarms. This can be done,
for example, by Dual Engine Connection (DEC), which is a sub-module
of engine #10.
[0296] The DEC method is a kind of compound association,
specialized for producing HVI-CP# pairs (HVI-CP pairs). FIG. 31 is
a diagram illustrating a DEC method in accordance with one
embodiment of the technology described herein. In the illustrated
example, the DEC is an inter-cloud association.
[0297] Referring now to FIG. 31, in this example a sample graphiti
1100 is applied with two possible nodes 1101 and 1102 applied as an
example. Important in some embodiments, is that those two nodes can
be applied in parallel as well as many other nodes, depending only
on computing processing power. Also four (4) exemplary clouds (or
databases) 1103, 1104, 1105, and 1106, may be applied. The nodes,
such as 1101 and 1102 may be identified by their Cyberphone numbers
(CP#).
[0298] The graphiti operation may be produced by a graph engine
#10. In parallel, the intra-cloud engine #2 may be configured to
select HVIs as yellow alarms. Finding the dual engine connection
(DEC) between such a CP# and an HVI, if successful, produces a red
alarm, or pre-alarm, if the training feedback is applied. Such a
connection can be readily located in the case of a regular person
who does not try to hide his/her identity. However, in the case of
the HVIC who purposely hides his/her identity, the situation may be
more complex. One challenge may be that such an HVIC, or HVI can
assume multiple identities with multiple IDs, such as: various
names, driver's licenses, passports, CP#s, etc., which he or she
might use only a few times. Nevertheless, he/she is using them
sometimes (including at times when a given graphiti exists within
the ISS computer system). Therefore, if the target population is
temporarily more narrowly defined, as in FIG. 29, for example, the
DEC can be identified, and the successful HVI-CP pair can be
produced. This is why each CP#, representing a given graphiti (such
as 1101, for example) may be configured to be "searching" all
clouds (1103, 1104, 1105, 1106, etc.) at the same time, through all
available lists of CP#s and equivalent names. Example lists can
include, for example, phone books, financial transactions, buy/sell
lists, affiliation lists, etc. This scanning process, which may in
some embodiments be relatively fast, is illustrated by arrows,
including the following arrows for node, 1101. These include
arrows, such as: 1107, 1108, 1109, 1110; same with the 2.sup.nd
node, 1102, and other nodes. Finally, some successful DEC pairs can
be found, such as 1111, for example, by identifying the CP# of node
1102, with HVI 1112.
[0299] Section 6: Network Inner Coherency (Inner Network)
[0300] 6.1 Inner Network Coherency
[0301] A summary of network inner coherency is now discussed.
Examples of this are described in greater detail in Sections 3.11
and Section 7. The inner coherency of an (adverse) network, such as
a terrorist or organized crime network, is introduced in order to
further improve the network search and detection. The network
members may, for example, be either individuals, (or HVICs), or
groups of individuals, called Groups of Interest (GOIs).
[0302] FIG. 47 is a diagram illustrating an example of an inner
coherency structure of adverse/hostile network 8000. The example
illustrated in FIG. 47 includes inter-GOI coherency coupling 8001
and intra-GOI coherency coupling 8002. The inter-GOI coherency
includes examples of the GOI's self-strengths (intensities)
I.sub.1, I.sub.2, I.sub.3, I.sub.4, denoted as 8003, 8004, 8005 and
8006 respectively. Accordingly, the number of network GOIs is N=4
in this example. Their sphere size illustrates their individual
strength, referred to as an I-value. As such, I.sub.1>I.sub.2,
for example. The inter-GOI coherence coupling, such as 8007 for
example, is represented by coherency matrix non-diagonal elements
T.sub.ij; i.noteq.j; together with intensities (I.sub.i)
constructing either diagonal kernels K.sub.i or non-diagonal
kernels H.sub.i. The matrix elements are generally non-symmetrical,
such that T.sub.12.noteq.T.sub.21, in general. The intra-GOI
structure 8002 in this example includes an inter-ego sphere 8008
and intra-ego sphere 8009 including unit-vectors 8010 and 8011,
respectively. These unit vectors 8010 and 8011 construct parallel
kernel vectors 8012 and 8013, respectively with .theta.-angle 8014
between them determining moral skew factor defined as cos(.theta.).
For zero-skew (.theta.=0) the intra-GOI structure is ignored by
analogy to "total daltonist" black and white view of any colorful
object or complete color blindness.
[0303] Further in the example of FIG. 47, both unit vectors, {right
arrow over (s.sub.4)} and {right arrow over (k.sub.4)} (for
4.sup.th GOI), are embedded on unit vector base with dimensionality
determined by moral senses. This base can be orthogonal or
non-orthogonal, by analogy to physical colors and RGB colors,
respectively. Also, by analogy to animal vision, the base
dimensionality can differ. For example, for human vision, the
number of color primaries is (typically) three (3), while for
animal vision the number of color primaries can be a number other
than three (3). For example, the European starling has four (4)
color primaries, the mantis shrimp (12), the honeybee (3), while
bichromatic insects have two (2) color primaries.
[0304] The moral skew factor, cos(.theta.), provides a more
objective view of the GOI's moral spectrum, which allows for more
precise parametric decision synopsis. This is because the
parametric decision projection can be different within intra-GOI
(intra-ego) as opposed to that within inter-GOI (inter-ego) views,
varying from the same views (.theta.=0) to a completely opposite
(orthogonal) view projection (.theta.=90.degree.). Then, the impact
of this decision on the overall network decision (defined by
weighted average, <S>) can be different. This is why the
inter-ego/intra-ego interactions have a vectorial character defined
in the simplest case by scalar product of vectors {right arrow over
(S)} and {right arrow over (K)} (or, rather, {right arrow over
(S.sub.i)} and {right arrow over (K.sub.i)}). The simple
explanation of this vectorial (not scalar) character is the fact
that "we see ourselves differently from how other people see
us."
[0305] Therefore, the decision process may be more objective if it
includes both inter-ego (inter-GOI), and intra-ego (intra-GOI)
projections to model the process.
[0306] 6.2 Comparison of Diagonal and Non-Diagonal Kernel
Vectors
[0307] The parametric decision weighted average formula for a
diagonal kernel vector (e.g., defined by Eq. (140)) may be more
compact and a more natural generalization of equivalent scalar
formula (5). Nevertheless, Eq. (145), representing the parametric
decision weighted average formula for a non-diagonal kernel vector,
is more basic than the diagonal one, and perhaps better represents
the moral skew effect (MSE) as explained below.
[0308] It is natural to assume that the unit vector, s,
representing the direction of the parametric decision vector {right
arrow over (S)}, is inclined to intra-ego senses, such as
self-interest, power, libido, etc. It is also natural to assume
that unit vector, s, represents a member (individual/GoI) strength,
while the unit vector, {circumflex over (k)}, represents mutual
coherency couplings, which may be defined by non-diagonal coherency
matrix, R.sub.ij, is more inclined to inter-ego (moral) senses
(tastes). Therefore, Eq. (141) May in various applications better
represent the moral skew factor/effect than Eq. (136), the latter
one representing diagonal kernel vector, {right arrow over
(K.sub.i)}.
[0309] 6.3 Moral Skew Effect and Psychoanalysis
[0310] The Moral Skew Effect (MSE) was approximately derived from
basic psychoanalysis concepts, such as those represented by Freud,
Adler, Yung, Fromm, and others. In particular, the Freudian
conflict between the super-ego and the id is approximately
equivalent to the ISS relation between the inter-ego and the
intra-ego (or the left and right brain hemispheres). Moreover, it
is evident that the moral senses represent the inter-ego point of
view, while self-interest senses represent the intra-ego point of
view. Furthermore, the basic self-interest senses include the
libido (Freud), power (Adler), and group security (Fromm) (which,
of course, to some extent overlap each other), as well as some
archetypes (Yung). Also, sub-consciousness, related to intra-ego
senses (tastes), can be individually related or they can be
GoI-like (Fromm). Therefore, the MSE psychoanalytic point of view
provides a more effective prognostic of certain particular social
events, described by the parametric decision process.
[0311] Section 7: Inner Network Analysis (Inner Network)
[0312] 7.1 Inter-Adverse Vs. Intra-Friendly
[0313] While the organized crime and terrorist networks are adverse
to outsiders (i.e., inter-network-adverse) they are, of course,
friendly amongst themselves (i.e., intra-network-friendly). The
latter aspect of the same organization (or, inner network) or the
"second side of the same coin" is the subject of this section. This
may be viewed, for example, as an extension and generalization of
Section 3.11. The Bayesian Truthing Inference (BTI) may also be
relevant here, where causation problems arrive in a sense of
Bayesian (directed and inverse) probabilities, while binary sensing
is generalized here to omninary sensing. The conditional (Bayesian)
probabilities characterize an "if, then" relation in which A-cause
and B-effect, can be described in the form:
p(B|A) (99)
This is a generalization of the Binary Sensor (BI) relation, such
as: (PFP)=p(S'|N), for example. In this section, some specific
exemplary BTI techniques are applied, such as, for example, a
Lossless Multi-Alarm method.
[0314] In order to prognose (prognosis is a less certain form than
prediction) certain events such as, for example, an uprising in
some country (or, state), strategic influence of emerging states,
role of social media, or effects of social messages, the system may
be configured to apply human learning/reasoning process. However,
in order to prognose such events by machine learning/reasoning
processes, either semi-automatically or automatically, it may be
beneficial to significantly narrow the context, such as for
example, by using the parametric decision learning/reasoning,
introduced in Section 3.11. This parametric decision approach is
generalized, in this section. Automatic training by minimization of
the cost function (which is similar to that in Section 5.1,
recognizing that the form of cost function may be different) may
also be applied.
[0315] 7.2 Parametric Statistical Ensemble
[0316] In Section 3.11, this document analyzes a single parametric
decision space, such as:
S.sub.i:S.sub.1,S.sub.2,S.sub.3, . . . ,S.sub.N (100)
where: i-index of certain individual, or group of interest
(GoI).
[0317] The 2.sup.nd l-index is assigned to decision value:
S.sub.l:S.sub.1,S.sub.2,S.sub.3, . . . ,S.sub.L (101)
[0318] Therefore, a given decision location may be related to
l-indices, while the decision location may be related to i-indices.
In Section 3.11, for example, Eq. (8) is related to i-indices,
while Eq. (13) is related to l-indices. Because a mostly Normal
Parametric Order (NPO) has been applied, as in FIG. 21, this
indexing ambiguity does not create problem. Otherwise, care should
be taken with this ambiguity. (However, the general avoidance of
this ambiguity may create double indexing). In this section, the
indexing is further generalized by introducing multiple parametric
decision spaces, using upper indices, such as:
S.sub.i.sup.(1):S.sub.1.sup.(1),S.sub.2.sup.(1), . . .
,S.sub.N.sup.(1) (102)
for example. FIG. 32 is a diagram illustrating an example of a
relation between i-indexing and l-indexing, in order to keep in
mind and control this ambiguity.
[0319] In FIG. 32, for the 4.sup.th-position (i=4), an
S.sub.2-value is provided. In order to avoid ambiguity, a different
symbol, for example V, may be used for the decision value. Then,
for the 4.sup.th position, as above, the following relation would
be obtained according to FIG. 32:
S.sub.4=V.sub.2 (103)
[0320] For ease of discussion, however, the notation used in FIG.
32 is maintained, keeping in mind that only Eq. (103) precisely
describes this double-indexing situation.
[0321] FIG. 33 is a diagram illustrating an example generalization
from a single parametric space, such as in Section 3.11, to a
multitude of parametric spaces. This can be shown, for example,
using the kernel notation as an example. In FIG. 33, the single
parametric space notation is shown at a), as in Eq. (100); and the
multiple parametric space notation is shown at b), as in Eq. (102).
In particular, the intensity 1500 does not have an upper index,
while the intensity 1501 does have an upper index "1," belonging to
parametric space 1. Likewise, the same can be said for the "with
coherency" matrix elements 1502 and 1503, as well as kernels 1504
and 1505.
[0322] Examples of a multitude of parametric spaces have been
introduced because, for a certain set/class of decisions, a given
parameter space may be more useful than the other. For example, if
a terrorist bombing is planned it could be planned in a "more
risky" or "less risky" fashion. Thus, a decision within the IED
network may be made based on some kind of voting logic process.
This voting will be made among the terrorist network members. For
example, there may be eight voting members (N=8), with indices:
i=1, 2, 3, . . . , 8. These members will typically have certain
strength intensities I.sub.1, I.sub.2, . . . I.sub.8, and mutual
couplings T.sub.ij, where T.sub.ij does not need to be equal to
T.sub.ji and T.sub.ii=1. In this particular case, the decision
spectrum, or decision scale may be made from "very low risk" to
"very high risk," as shown in FIG. 34.
[0323] As this example serves to illustrate, the decision space
scale from "very low risk" to "very high risk," for example, would
be less adequate than the (RISK)-parametric decision scale.
[0324] FIG. 35 is a diagram illustrating an example of a parametric
statistical ensemble 1600 including various Parametric Decision
Realizations
PDR.sub.1.sup.(1):PDR.sub.2.sup.(1),PDR.sub.3.sup.(1), . . .
(104)
representing such decision processes. As discussed above (terrorist
bombing, for example), these decision processes could be denoted as
PDR.sub.2, while an upper index (1) may be used to denote the
(RISK) parametric decision, for example, as shown in FIG. 34.
Therefore, these PDRs 1601, 1602, 1603 may constitute a Parametric
Decision Ensemble PDE(1) denoted as 1604, while the parametric
decision scale S(1) may be denoted by 1605, as well as coherency
matrix elements 1606. While these two classes of parameters 1605
and 1606 may have specific values assigned to ensemble 1600, the
intensities I.sub.i denoted as 1607 may be rather invariant.
Accordingly, they do not have an upper index (1). Therefore, the
intensities 1607 can constitute other Parametric Decision Ensembles
(PDEs), such as, for example, PDE.sup.(2) 1608 with its coherency
matrix elements 1609.
[0325] The statistical weighted mean value, <S.sup.(1)>, may
be ensemble-averaged, in the form:
{<S.sup.(1)>} (105)
where { . . . } is the symbol of ensemble average. This
ensemble-averaged weighted mean, 1610, is result of four (4)
connections (first three illustrated by arrows) 1611, 1612, 1613,
and 1614, resulting in a mean average for each PDR, as defined by
Eq. (8). The ensemble-average (possibly weighted) may result in Eq.
(105).
[0326] 7.3 Parametric Prognosis
[0327] FIG. 36 is a diagram illustrating an example of a simple
parametric prognosis in accordance with one embodiment of the
technology described herein. Particularly, the example illustrated
in FIG. 36 may be obtained by applying a Parametric Decision
Ensemble, such as that illustrated in FIG. 35.
[0328] In the example of FIG. 36, the already constituted ensemble
3, with three realizations, 1700, 1701, and 1702, is shown. This
ensemble has parametric scale, 1703, a coherency matrix structure,
1704, and an intensity structure, 1705. All these ensemble elements
may be used to produce four (4) connections (causations), 1706,
1707, 1708, 1709, which, in turn, can produce the ensemble average,
1710. Then, if the new realization, 1711, also belongs to this
ensemble, it can be inferred that the new connection, 1712,
produces the same (or similar) result, 1710. This simple parametric
prognosis can work approximately, assuming that one of the
constituted realizations, 1700, 1701, 1702, has been experimentally
verified recently, for checking purposes.
[0329] A more complex, but also a more precise parametric prognosis
can be obtained using the cost function minimization process. This
process can be similar to that shown in FIG. 30, except that the
cost function definition is now different. For example, it may be
defined as a module of difference between weighted mean
experimental and theoretical values. In various embodiments, the
Parametric Cost Function (PCF) is given by
(PCF)=|<S>.sub.TH-<S>.sub.EXP| (106)
where | . . . | is module symbol, and the procedure is illustrated
in FIG. 37, where ensemble indices have been omitted, for
clarity.
[0330] In FIG. 37, the theoretical parametric mean value, 1850, may
be constructed from kernel, 1851, and a parametric scale, 1852.
This can be done, for example, based on Eqs. (8), (9), and (13), by
using either intelligence knowledge or an expert query. Then, an
experimental value, 1853, may be obtained by experiment, 1854, for
example, using the method as in FIG. 35. Then, Eq. (106) is
applied, in order to obtain the PCF, 1855. Then, the PCF
minimization procedure may be applied in a manner similar to that
illustrated in FIG. 30.
[0331] 7.3.1 Parametric Intensity Prognosis
[0332] FIG. 38 is a diagram illustrating an example of a more
global procedure of prognosis parametric intensity set in
accordance with one embodiment of the technology described herein.
The example shown in FIG. 38 may be accomplished by applying a
premise that the strength intensity set, is (entirely or almost)
invariant to parametric scale. This set is defined in this example
by three (3) exemplary parametric ensembles, 1800, 1801, and 1802.
These ensembles may be used to generate three ensemble averages,
1803, 1804, and 1805, respectively. It can be assumed as an
approximation that all three results have been generated on the
same parametric intensity set, 1806. Therefore, using an inverse
procedure, characterized by connections, 1807, 1808, 1809, 1810,
1811, and 1812, the prognosed value, 1813, can be obtained through
computation. The prognosed value may be obtained fairly close to
the real value, 1806. In this example, the continuous lines 1807,
1808, 1809, denote a procedure based on the PCF-minimization, while
the broken lines 1810, 1811, 1812, denote a procedure obtained
without PCF-minimization.
[0333] 7.4 Coherent Coupling Engineering
[0334] The parametric ensemble engineering (PEE) concept, in
general, and Coherent Coupling Engineering (CC-Engineering)
concept, in particular, may be applied in order to probe and
construct various parametric ensemble models, either theoretically
(by design), or practically (by experiment), or both. The term
CC-engineering arises from the fact that coherent coupling matrix
elements, T.sub.ij, are easiest to manipulate, because they are
most flexible, or most space/time-variant, while parametric
intensities, I.sub.i, are rather rigid, and may in some
circumstances be rather difficult to manipulate. In general, the
typical parametric ensemble may contain four-types of data:
STRUCTURAL:(K.sub.i;I.sub.i,T.sub.ij) (107a)
INPUT:Context,Ensemble Realizations (107b)
PARAMETRIC:S (107c)
OUTPUT:<S>,{<S>} (107d)
[0335] FIG. 39 is a diagram illustrating an example of these for
data types in accordance with one embodiment of the technology
described herein. Referring now to FIG. 39, example of a Parametric
Decision Ensemble (PDE) architecture, and CC-Engineering is shown.
This example includes an Input data interface, 1900; sub-system
structure, 1901; a parametric interface, 1902; an algorithm, 1903,
and an output data interface, 1904. The input interface, 1900, may
be configured to insert input data, in the form of Parametric
Decision Realizations (PDRs), such as: PDR.sub.1, 1905, PDR.sub.2,
1906, and PDR.sub.3, 1907. This input data description may be
inserted into a sub-system structure, 1901; thus, defining the
parametric intensity set, I.sub.i, 1908, and coherent coupling
matrix elements, T.sub.ij, 1909, summarized into kernel, 1910, for
the ith-member. This process may be repeated for each ith-member,
up to a quantity of N members. The parametric S-set, 1911, may be
introduced in parallel to both the structure, 1901, and sub-system
algorithm, 1903. After algorithmic computing, the output data,
1912, may be produced.
[0336] CC-Engineering Procedure.
[0337] The CC-Engineering interface 1913 in this example introduces
variations of T.sub.ij-matrix components, 1909, according to a
pre-described procedure. In this way, both engineering and probing
scenarios may be realized. The connection 1914 is directed mostly
to CC-matrix elements, T.sub.ij, because they may be very flexible
and time/space-variant, depending on type of stimulation (this is a
characteristic feature of members' mutual relations, defined by
Coherency Matrix, T.sub.ij). In a similar way, the system may be
configured to provide probing by synchronizing various PDRs, with
related variations of T.sub.ij-matrix elements, as discussed
below.
[0338] Coherency Matrix Variations.
[0339] In order to better understand how the weighted mean,
<S>, a change under stimulation (probing), the weight,
w.sub.i, changes may be analyzed as defined previously in the
form:
w i = K i i = 1 N K i ; i = 1 , 2 , 3 , , N ( 108 )
##EQU00028##
Then, by differentiating (in approximation of small changes) this
formula, the following expression for w.sub.i-change,
.DELTA.w.sub.i, may be derived:
.DELTA. w i = .DELTA. K i i = 1 N K i + K i [ - ( 1 i = 1 N K i ) 2
i = 1 N .DELTA. K i ] = = .DELTA. K i i = 1 N - w i ( i = 1 N
.DELTA. K i i = 1 N K i ) ( 109 ) ##EQU00029##
[0340] Therefore, the relative change (in %), is
.DELTA. w i w i = .DELTA. K i w i i = 1 N K i - i = 1 N .DELTA. K i
i = 1 N K i ( 110 ) ##EQU00030##
and, finally, the following expression for weight relative change
may be obtained:
.DELTA. w i w i = .DELTA. K i K i - i = 1 N .DELTA. K i i = 1 N K i
( 111 ) ##EQU00031##
[0341] Thus, the relative weight change for the ith-member is a
difference of two terms: the 1.sup.st local term depends on
relative change of the ith-kernel only, while the 2.sup.nd global
term, depends on all ensemble values. As this example illustrates,
those terms are small quantities of the same order, and they have
opposite signs. Thus, sometimes, they may cancel or almost cancel
each other.
[0342] 7.5 Application Scenarios for PDE Systems
[0343] Three (3) application scenarios are presented for
illustration of the PDE systems, including such diverse areas as:
social geopolitics, social media, and Organized Crime Networks, for
example. All of them may be applied for the same PDE modeling,
following FIGS. 35 and 39.
[0344] SCENARIO #1 (Social Geopolitics). Emerging States.
[0345] Question: What is the current strength of a number of
emerging states (countries)?
[0346] In order to answer this question, the system may be
configured to apply a Parametric Intensity Prognosis scheme, such
as that shown in FIG. 38, with multi-parametric space. In such a
case, a number of equations defining the weighted means <S>
may be used. It can be assumed that each equation represents a
single Parametric Decision Ensemble (PDE). It can be further
assumed that a number of states (not only emerging ones) to be
considered is equal to 100; i.e., N=100
[0347] Then, a number of the PDEs, should be also equal to at least
100. If the number of the PDEs is not sufficient, the system may be
configured to apply Parametric Decision Realizations (PDRs), and
ensemble averages may be replaced by weighted means (by
"realization", we mean a given ensemble realization), in the form
(M is a number of PDRs):
<S.sup.(1)>=f.sub.1(I.sub.i.sup.(1),T.sub.ij.sup.(1),S.sup.(1))
(112a)
<S.sup.(2)>=f.sub.2(I.sub.i.sup.(2),T.sub.ij.sup.(2),S.sup.(2))
(112b)
<S.sup.(3)>=f.sub.3(I.sub.i.sup.(3),T.sub.ij.sup.(3),S.sup.(3))
(112c)
. .
. .
<S.sup.(M)>=f.sub.M(I.sub.i.sup.(M),T.sub.ij.sup.(M),S.sup.(M))
(112d)
where, in the simplest case, all functions f.sub.( . . . ), are
identical:
f.sub.1=f.sub.2=f.sub.3= . . . =f.sub.M (113)
and, represented by Eqs. (8), (9), and (10), in the form:
< S ( m ) >= i = 1 N w i ( m ) S i ( m ) ; w i ( m ) = K i (
m ) i = 1 N k i ( m ) ( 114 a ) and , K i ( m ) = j = 1 N T ij ( m
) I i ( m ) I j ( m ) ( 114 b ) ##EQU00032##
i.e., the f-function, is
f ( I i ( m ) , T ij ( m ) , S ( m ) ) = i = 1 N w i ( m ) S i ( m
) ( 115 ) ##EQU00033##
[0348] It can be assumed that all coherency matrix elements are
known, and that these may be found from experiment (e.g., by
observing a large number of geopolitical situations). It may also
be assumed that all S-parameters have been given (assigned, for
each particular geopolitical situation). Also, a further assumption
may be that all weighted averages have been found (i.e., by
studying all available geopolitical documents, journals, etc.).
Therefore, the number of unknowns is N:
I.sub.1,I.sub.2,I.sub.3, . . . I.sub.N (116)
[0349] This is because it can be assumed as before that the
parametric intensities are rather space/time invariant (at least
within a given time internal); i.e., their upper indices have been
cancelled, as in Eq. (116). Now, assuming that:
M.gtoreq.N (117)
then, the problem is numerically solvable. Therefore, as a result,
the strengths of all states (not only emerging states) may be
determined as defined by their parametric intensities, as in Eq.
(113). For example, if it is determined that:
I.sub.50>I.sub.72 (118)
then, the 50.sup.th-country is stronger than the 72.sup.nd country
(state), at least, within the system of ensembles and situations,
considered within this application scenario.
[0350] SCENARIO #2 (Social Media). Impact of Messages
[0351] Question: What is impact of specific social messages
transmitted through the Internet?
[0352] In order to answer this question, which is simpler than that
in SCENARIO #1, the system may be configured to apply the Simple
Parametric Prognosis scheme, such as that shown in FIG. 36, for
example. It can be assumed that, from experience, that parametric
intensities, and coherent couplings, T.sub.ij, are known. These can
be those of all centers of influence for a given PDE, which
represents the specific message in question. Based on previous
experience, the ensemble average of the parameter of interest (POI)
may be numerically calculated. This POI could represent, for
example, risk, cost, speed, radicalization level, etc. Then, in
this simplest case, the ensemble average obtained from previous
experience may be used. For example, if the PDE of Interest (PDEol)
is denoted by upper index (3), as in FIG. 36, then our answer,
is
{<S.sup.(3)>} (119)
[0353] The higher this value is, the higher the impact according to
a given parametric scale.
[0354] In the more complex cases, a structure for Parametric Cost
Function (PCF) may be applied as in FIG. 37, for example.
[0355] SCENARIO #3. (Organized Crime Network).
[0356] Election of the Leader.
[0357] Question: Who, among the Organized Crime Network members,
will be elected as a new leader?
[0358] This problem is similar to that of SCENARIO #1, and that it
may be a multi-step analysis. In the 1.sup.st step, the system
applies the same approach as in SCENARIO #1. As an output, the
system obtains a narrow set of leader candidates. Then, in the
2.sup.nd step, the system applies the methodology of the Lossless
Multi-Alarm (LMA) method, as shown in FIG. 29. This means, that, in
the 1.sup.st step, the system should preferably have very low
target losses, or the Probability of False no-Alarm (PFnA) is very
low; while the Probability of False Alarm (PFA), or Probability of
False Positives (PFP), are high. In the 2.sup.nd step, the system
defines new kernel components, K.sub.i, using available police
search data. These K.sub.i-components, especially including
coherency matrix elements, T.sub.ij, are more precisely defined
than in the 1.sup.st step because they are limited to a narrower
context; i.e., a much lower number of the leader candidates are
considered in the 2.sup.nd step. As a final result, the system
obtains one final candidate for the leader position.
[0359] 7.6 Phenomenology of PDE System
[0360] 7.6.1 Origin of the Systems and Methods Described Herein
[0361] For purposes of explanation, consider in more detail the
phenomenology of the Parametric Decision Ensemble (PDE) system and
method. Because the PDE concept is a rather complex one, the
phenomenology of this system may be explained using two analogies:
physical and social. The origins of the PDE concept can be traced
to physical optics (optical interference), moral psychology, animal
vision, and Bayesian Truthing Inference (BTI)--the latter one in a
more actional sense, by applying Lossless Multi-Alarm Method,
illustrated in FIG. 29, for example. The physical optics origin is
demonstrated by applying the truncated interference term, in kernel
definition, as in Eq. (10). ("Truncated" means that trigonometric
oscillatory term has been omitted.) The moral psychology origin
requires further explanation.
[0362] Moral Psychology Origin.
[0363] Moral psychology applies moral analogs of human tastes such
as: sweet, sour, dry, and salty. These "moral tastes" are, for
example: care, liberty, fairness, loyalty, authority, and sanctity.
Their composition defines human morality, which can be categorized,
for example, within three (3) basic political categories: liberal,
libertarian, and conservative. (While, in the single individual
case, the moral psychology subject may be considered; in the social
group case, the moral sociology subject is considered.)
[0364] In order to better understand the PDE system, it is useful
to consider two analogies:
[0365] A. Physical (Thermodynamic Gas of Particles)
[0366] B. Social (Moral Sociology)
[0367] FIG. 40 is a diagram illustrating an example of the
phenomenology of the PDE system. Referring now to FIG. 40, in this
example the PDE Phenomenology 3020 is illustrated as including the
PDE concept origins 3021 and analogies 3022. The PDE concept
origins 3021 may include optical coupling, 3023, applicable for
kernel, K.sub.i, definition; moral psychology 3024 helpful in
defining parametric space; Bayesian Truthing Interference (BTI)
3025 producing some actionable techniques for the PDE system; and
animal vision 3028. The PDE concept analogies 3022 may include
thermodynamic gas analogy 3026 and moral sociology analogy 3027;
i.e., moral psychology concept applicable to social group.
[0368] Animal Vision Origin.
[0369] Animal vision origin may also contribute to the PDE concept
by producing a vectorial base. The vectorial base may be both
orthogonal and non-orthogonal, for a Parametric Decision Vector,
{right arrow over (S)}. The analog of an orthogonal base may be
obtained from physical colors, defined by wavelengths; while the
non-orthogonal base may be obtained from RGB (Red-Green-Blue)
colors such as those of an animal vision model 3028.
[0370] 7.6.2 Thermodynamic Gas Analogy
[0371] In FIG. 41, examples of three (3) gas mixtures, 6000, 6001,
and 6002, illustrated in FIGS. 41(a), 41(b), 41(c), are shown.
These examples represent three types of molecules, and are denoted
by denoted by circle 6003; triangle 6004 and square 6005,
respectively. In this example, each molecule moves with velocity
vector, {right arrow over (v)} denoted by an arrow, such as 6006,
for example. The arrow's direction represents a velocity direction,
while speed value, v, or |{right arrow over (v)}|, is represented
by the arrow length. For example, velocity 6007 is larger than
velocity 6008.
[0372] In this example, these three (3) gases have the same number
of three (3) types of molecules, and are located in the same size
cubes 6009, 6010, and 6011, with the same volume equal to d.sup.3,
where d-linear cube size, 6012. The molecules refract from cube
walls, and collide with other molecules. The collisions are denoted
by molecule pairs, such as 6013, for example, and double arrows,
such as 6014, represented by Coherency Matrix elements, T.sub.ij,
for example.
[0373] For analogy purposes, v.sup.2-speed square may be used as an
analog of the S parameter
v.sup.2S (120)
[0374] because the v.sup.2-parameter is valid for all three cubes,
the analogy should be restricted to the single parametric space,
and single ensemble, only. The 2.sup.nd analog must be between
molecule mass, m.sub.i, and kernel K.sub.i:
m.sub.iK.sub.i (121)
[0375] Thus, this example illustrates that there are only three (3)
types of kernels due to graphical symbol limitation. However, the
i-index is applied to all molecules in the cube; thus, N is the
number of all molecules in the cube (here, N=15). By way of
analogy, it can be seen that each cube represents a Parametric
Decision Realization (PDR), while all three of them represent a
single ensemble (PDE).
[0376] Because this is discussed in terms of a thermodynamic gas
model, (for purposes of analogy), some thermodynamic function (or,
function of state) may be considered as an analog of either
weighted mean: <S>, or ensemble average: {<S>}. For
example, assume the simplest case when all molecules are identical
and there is no interaction between them:
I.sub.i=constant; T.sub.ij=0 (122ab)
[0377] Then, the average kinetic energy, is
E k = 1 N i = 1 N mv i 2 2 = 3 2 kT ( 123 ) ##EQU00034## [0378]
where N is the number of particles, T is the absolute temperature
(in Kelvin degrees), and k is Boltzmann's constant. Therefore, an
analogy may be drawn between <S> and the absolute temperature
thermodynamic function.
[0379] However, in the case in which condition (122a) is not
satisfied, this simple analogy becomes more complicated because the
PDE mean has the form:
S = i = 1 N I i S i i = 1 N I i ( 124 ) ##EQU00035##
[0380] By way of simplification, instead of Eq. (124), the
following simple formula may be considered:
S = I i S i i I i ( 125 ) ##EQU00036##
which is defined as exactly equivalent to Eq. (124). Therefore, the
summary term in the denominator precludes application of the
thermodynamic gas analog. In order to save this analogy, the
charged gas particles may be considered. Thus, the interactive
kernel term may be an analog to potential energy term, U.sub.ij, in
the form:
A q i q i r ij .revreaction. T ij I i I j ( 126 ) ##EQU00037##
where, q.sub.i--particle charge, r.sub.ij--mutual distance, and
A-proportionality constant. However, the summary term in
denominator, is
i K i ( 127 ) ##EQU00038##
which precludes this analogy. Indeed, this summary term Eq. (127)
is a global term that more fits to wave optics rather than to
mechanical model such as thermodynamic gas, for example. This is
not surprising, because at the beginning the optical coupling model
was applied.
[0381] 7.6.3 Moral Sociology Analogy
[0382] The moral sociology scenario be considered as a
generalization of moral psychology for social groups (groups of
interest), rather than for individuals. After studying this analogy
further, however, it may be concluded that this analogy fits well
to narrow contexts such as scenarios #1 and #3 (i.e., when the goal
is to select some strong candidates). Moreover, this analogy
provides an important clue, which comes from an animal vision
analogy 3028 such as that, for example, shown in FIG. 40. In order
to obtain a broader context analogy, it is important to the treat
decision parameter, S, as a vector, {right arrow over (S)}, and/or
tensor S.sub.kl, embedded onto the orthogonal, or non-orthogonal
base of several moral tastes, with the addition of some primitive
tastes, such as power, security and/or libido, for example. The
analogy between a non-orthogonal parametric base, and RGB animal
(including, human) vision where any color is defined in
non-orthogonal base (this is, because, the RGB-spectra overlap each
other), as shown in FIG. 42, for 2D-space, for simplicity.
[0383] For the PDE, the Parametric Decision Vector (PDV) base may
be six-dimensional, seven or eight-dimensional, or higher. Some
parametric decisions made be stronger if the base unit vectors tend
to the same direction. Also, the scalar product of such vectors,
may have a lower value even if these vectors are large but close to
normal to each other, as shown in FIG. 43.
[0384] This is because the scalar product of two vectors: {right
arrow over (S)}.sub.1, and {right arrow over (S)}.sub.2, is
{right arrow over (S)}.sub.1{right arrow over (S)}.sub.2=|{right
arrow over (S)}.sub.1.parallel.{right arrow over (S)}.sub.2| cos
.alpha. (128)
[0385] where .alpha.-angle between these two vectors, as shown in
FIG. 43.
[0386] 7.7 Moral Skew Factor
[0387] 7.7.1 Inter-Ego Vs. Intra-Ego
[0388] In the previous sections, inter-group coherent coupling was
introduced in an environment based on an interaction between
group/network members. In this section, a more internal type of
coherency related to moral psychology/sociology (or,
psychoanalysis) (i.e., intra-individual relations) is introduced.
This new type of coherency may be used to define a moral skew
factor. In the case of a single individual, for example, this skew
factor may be a consequence of a Freudian conflict between left and
right brain hemispheres, defined by Freud as a conflict between the
id and the super ego. In a broader cycle analytical sense, this
conflict is referred to as the conflict between inter-ego and
intra-ego.
[0389] In various embodiments, this conflict may be manifested as a
skew effect between parametric decision, S.sub.i, and kernel,
K.sub.i. This moral skew factor may be mathematically modeled as a
scalar product of two vectors {right arrow over (S.sub.i)} and
{right arrow over (K.sub.i)}: wherein a higher skew higher skew
results in a higher angle, .theta., between these vectors. In the
extreme case, the scalar product, {right arrow over
(S.sub.i)}{right arrow over (K.sub.i)}, can be equal to zero, even
if the vectors' values (lengths), |{right arrow over (S.sub.i)}|
and |{right arrow over (K.sub.i)}|, are large. This is when,
.theta.=90.degree..
[0390] 7.7.2 Unit Vector Bases
[0391] Both vectors {right arrow over (S.sub.i)} and {right arrow
over (K.sub.i)} may be defined in the same unit vector base which
can be either orthogonal, or non-orthogonal, constructed of unit
vectors; in 3D-space, for example:
.sub.x, .sub.y .sub.z;| .sub.x|=|e.sub.y|=| .sub.z|=1 (129ab)
[0392] The unit-vector-space may be multi-dimensional, with the
number of dimensions being equal to two, three, or higher. For
example, for five (5)-dimensions, the unit-vector-space is
5D-space, or 5-space.
[0393] 7.7.3 Primary Color Analogies
[0394] Primary color analogies are very useful to illustrate
differences between orthogonal and non-orthogonal
unit-vector-bases. For example, physical quasi-monochromatic
colors, defined by central wavelengths, are orthogonal. However,
the animal vision is based on RGB (red-green-blue) color primaries,
or RGB primary colors, with overlapping wavelength spectra. This
phenomenon, in vector functional analysis, is equivalent to the
fact that functional vectors representing overlapping spectra are
not orthogonal to each other; thus, creating a non-orthogonal unit
vector base (vector functional analysis is applied in quantum
mechanics, for example).
[0395] 7.7.4 Scalar Product of Parametric Decision and Kernel Unit
Vectors
[0396] FIG. 44 is a diagram illustrating an example of a scalar
product of a parametric decision and kernel unit vectors in an
orthogonal base. In FIG. 44, the scalar product a) of two unit
vectors s 5001 and {circumflex over (k)} 5002 is presented in an
orthogonal base having three unit vectors .sub.x 5003; .sub.y 5004;
and .sub.z 5005, thus creating a 3D-space. These vectors 5001 and
5002 are skewed by angle .theta. 5006. This base is orthogonal
because all three angles between the unit vectors 5003, 5004 and
5005 are right-angles (orthogonal) such as 5007, 5008 and 5009 for
example.
[0397] The primary color analogy is illustrated at b) and includes
three orthogonal (non-overlapping) wavelength spectra 5010, 5011,
and 5012. The horizontal axis, .lamda., represents central
wavelength values such as .lamda..sub.1, .lamda..sub.2, and
.lamda..sub.3, for example. The exemplary .lamda..sub.3-central
wavelength 5013 can represent the 630 nm wavelength (red color),
for example.
[0398] In such an orthogonal base, the unit vector, s, is
represented by:
s=a.sub.x .sub.x+a.sub.y .sub.y+a.sub.z .sub.z (130)
where:
a.sub.x.sup.2+a.sub.y.sup.2+a.sub.z.sup.2=1 (131)
and:
| .sub.x|=| .sub.y|=| .sub.z|=1; .sub.x .sub.y=0;
.sub.x .sub.z=0; .sub.y .sub.z=0 (132a; 132b; 132c; 132d)
[0399] Eq. (131) describes the unit vector property; Eq. (132a),
describes unit base vectors; and Eqs. (132b,c,d) describe
orthogonality of unit base vectors. Similarly, the unit vector
{circumflex over (k)} is represented by:
{circumflex over (k)}=b.sub.x .sub.x+b.sub.y .sub.y+b.sub.z .sub.z
(133)
where:
b.sub.x.sup.2+b.sub.y.sup.2+b.sub.z.sup.2=1 (134)
[0400] In FIG. 45, the scalar product of s and {circumflex over
(k)}-vector is presented in a non-orthogonal base.
[0401] FIG. 45 illustrates the scalar product a) of two unit
vectors, {circumflex over (k)}, and s, 5020, and 5021, skewed by
angle .theta. 5022. In this example, this is embedded on
non-orthogonal unit vector base, when the base unit vectors 5023,
5024, and 5025 are not orthogonal (not perpendicular).
[0402] The primary color analogy b) is also illustrated, where
color primaries 5026, 5027, and 5028 are overlapping, with
overlapping hatched areas 5029, and 5030. Equations describing the
unit vectors s and k are similar to Eqs. (130-132), except, Eqs.
(132bcd) are not satisfied.
[0403] For clarity of description, the further mathematics, based
on vector algebra, are provided for the orthogonal base.
[0404] The scalar product of two unit vectors, s and {circumflex
over (k)}, is
s{circumflex over (k)}
a.sub.xb.sub.x+a.sub.yb.sub.y+a.sub.zb.sub.z=|s.parallel.{circumflex
over (k)}|cos .theta.=cos .theta. (135)
[0405] This is, because, according to Eqs. (127) and (130)
|s|=|{circumflex over (k)}|=1 (136)
[0406] i.e., s and {circumflex over (k)}-vectors are, indeed, unit
vectors.
[0407] 7.7.5 Scalar Product of Parametric Decision and Kernel
Vectors
[0408] The scalar product of a Parametric Decision vector and a
kernel vector is not automatically a generalization of the previous
section describing scalar product of equivalent unit vectors. In
fact, it requires further analysis, presented below.
[0409] 7.7.6 Diagonal and Non-Diagonal Kernel Vectors
[0410] Diagonal Kernel Vector.
[0411] The diagonal kernel vector is defined as such vector that
the coherency matrix has usual diagonal form, defined
previously:
{right arrow over (K.sub.i)}=K.sub.i (137)
where K.sub.i is kernel scalar, defined by Eq. (11) and is unit
vector defined by Eq. (133). In parallel, the parametric decision
vector, {right arrow over (S.sub.i)}, is defined as:
{right arrow over (S.sub.i)}=S.sub.i (138)
where S.sub.i is parametric decision scalar, as in Eq. (5), and is
unit vector defined by Eq. (130).
[0412] Therefore, the scalar product of kernel vector, {right arrow
over (K.sub.i)}, and parametric decision vector {right arrow over
(S.sub.i)}, is
{right arrow over (S.sub.i)}{right arrow over
(K.sub.i)}=S.sub.iK.sub.i cos .theta..sub.i (139)
where .theta..sub.i is moral skew factor for ith network member,
and the weighted average, is
S = i = 1 N S i K i cos .theta. i i = 1 N K i cos .theta. i = i = 1
N S -> i K -> i i = 1 N K i cos .theta. i ( 140 )
##EQU00039##
[0413] Ignoring the moral skew factor, .theta..sub.i, is, according
to the color analogy, equivalent to a "blind vision" ignorance of
colors, by seeing only in black-white.
[0414] Moral Skew Factor Interpretation.
[0415] The moral skew factor interpretation is based on a conflict
between inter-ego and intra-ego. According to the ISS model, both
inter-ego and intra-ego may be embedded in the unit vector base, ,
, , . . . , defined by moral senses. The moral senses' base may be
a multi-dimensional base with a number and type of dimensions
depending. This number and type may depend on individual parametric
decision space, etc. ("individuals" may include not only
individuals in narrow sense (such as humans), but also in a broader
sense, as individuals' group of interest). For example, in recent
conventional systems "the righteous man" concept, there are six (6)
moral senses such as: cure/harm; liberty/oppression;
fairness/cheating; loyalty/betrayal; authority/subversion; and
sanctity/degradation. In the ISS language, the moral sense unit
vector base, such as the example shown in FIGS. 44 and 45, would be
in the 6D-space. However, the moral skew factor concept introduced
here is more general and differs in such a sense. Particularly, it
adds at least one more dimension, namely, self-interest/altruism.
Accordingly, this space would be 7D. The 1.sup.st six (6) moral
senses may be referred to as inter-ego senses, while the 7.sup.th,
8.sup.th, etc. self-interest may be referred to as intra-ego
senses. In the ISS model, the number of inter-ego senses can be
different from six (6), and they can be of different types. In
addition, the number of inter-ego senses can be greater than one,
and different, in general. Moreover, some embodiments can be
distinguished as using a combination with a parametric decision
model in such a sense that the parametric decision unit vector, s,
is dominated by intra-ego senses (i.e., its intra-ego components:
a.sub.x, a.sub.y, a.sub.z, etc., are large for those senses). In
addition, the kernel unit vector, {right arrow over (K)}, may be
dominated by inter-ego sense.
[0416] Therefore, the moral skew factor is typically going to be
large if there is less conflict between the inter-ego and intra-ego
senses, and vice versa. The mathematical modeling of this conflict
herein is a novel, unifying psychoanalysis concept, with a moral
sense sociologic concept and a self-interest moral sense.
[0417] Non-Diagonal Kernel Vector.
[0418] A new non-diagonal kernel vector as which may be based on
non-diagonal coherency matrix, R.sub.ij, may be defined as:
R ij = { T ij , i .noteq. j 0 , i = j ( 141 ) ##EQU00040##
[0419] Then, the non-diagonal kernel vector, {right arrow over
(H)}, has the form:
{right arrow over (H)}.sub.i=s.sub.iI.sub.i+{circumflex over
(k)}.sub.iG.sub.i (142)
where G.sub.i scalar has the form:
G i = j = 1 N R ij I i I j ( 143 ) ##EQU00041##
This scalar is called a non-diagonal kernel.
[0420] Accordingly, in contrast to a diagonal kernel vector, the
intensity scalar, I.sub.i, is attached to the s.sub.i-unit vector,
rather than to the {circumflex over (k)}.sub.i-unit vector.
Therefore, the scalar product of {right arrow over (S)}.sub.i and
{right arrow over (H)}.sub.i vectors, is
{right arrow over (S)}.sub.i{right arrow over
(H)}.sub.i=(s.sub.iI.sub.i+{circumflex over
(k)}.sub.iG.sub.i)(s.sub.iS.sub.i)=I.sub.iS.sub.i+G.sub.iS.sub.i
cos .theta..sub.i (144)
and Eq. (139) is modified into the following equation:
S = i = 1 N S -> i H -> i i = 1 N ( I i + G i cos .theta. i )
= i = 1 N S i ( I i + G i cos .theta. i ) i = 1 N ( I i + G i cos
.theta. i ) ( 145 ) ##EQU00042##
[0421] This represents the parametric decision weighting average
for the non-diagonal kernel case in accordance with several
embodiments. According to Eq. (145) the weight satisfies the
normalization condition.
[0422] Hybrid Case.
[0423] In such a case, elements of diagonal and non-diagonal kernel
vector cases are combined. This may be accomplished by applying a
weighted average of Eqs. (140) and (145).
[0424] 7.7.7 Quantitative Analysis of the Moral Skew Factor
[0425] For clarity of description, the 2-D orthogonal base is
considered. In this example, the base represents only two
dimensions: the x-coordinate representing inter-ego moral sense;
and the y-coordinate representing intra-ego moral sense. Then, the
{circumflex over (k)}-unit vector is more inclined to the x-axis,
while the s-unit vector is more inclined to the y-axis, as shown in
the example of FIG. 46. Assume that a parametric decision auxiliary
vector, {right arrow over (s)}, has y-component, a.sub.y', 5-times
larger than its x-vector component, a.sub.x'. Assume also that the
kernel auxiliary vector, {right arrow over (k)}, has an
x-component, b.sub.y', 3-times larger than its y-component,
b.sub.y'.
[0426] FIG. 46 is a diagram illustrating the value of such a moral
skew factor. In this figure, for clarity of discussion, a whole
inter-ego unit vector base has been reduced to single x-coordinate,
representing group-interest moral senses (tastes). The same has
been done for the intra-ego unit vector base, which has been
reduced to single y-coordinate representing the self-interest moral
tastes/senses such as power, libido, self-preservation, etc.
[0427] In the example shown in FIG. 46, the quantitative analysis
of the moral skew factor is illustrated. This example includes
auxiliary vector {right arrow over (s)} 7000 and auxiliary vector
{right arrow over (k)} 7001. These auxiliary vectors {right arrow
over (s)} and {right arrow over (k)} are parallel to unit vectors s
7002 and {circumflex over (k)} 7003, respectively. The orthogonal
base is shown in 2D space represented by unit vectors 7004 and
7005. Because vector 7000 is arbitrarily chosen to be only parallel
to unit vector 7002, it can be assumed that: a.sub.x'=1 a.sub.y'=5.
Thus, its module (length) is {square root over
((a.sub.x').sup.2+(a.sub.y').sup.2)}= {square root over (1+25)}=
{square root over (26)}. Therefore the unit vector s 7002
components are:
s ^ = ( a x , a y ) = ( 1 26 , 5 26 ) ( 146 ) ##EQU00043##
[0428] Similarly, the auxiliary vector 7001 has a length {square
root over ((b.sub.x').sup.2+(b.sub.y').sup.2)}= {square root over
(36+4)}= {square root over (40)}; and the unit vector {circumflex
over (k)} 7003 has the following components:
k ^ = ( b x , b y ) = ( 6 40 , 2 40 ) ( 147 ) ##EQU00044##
[0429] Therefore, the moral skew factor, cos(.theta.), where
.theta.-angle is denoted by 7006, is
cos .theta. = s ^ k ^ = a x b x + a y b y = ( 1 26 ) ( 6 40 ) + ( 5
26 ) ( 2 40 ) = ( 0.196 ) ( 0.969 ) ++ ( 0.98 ) ( 0.316 ) = 0.186 +
0.31 + 0.496 ( 148 ) ##EQU00045##
and the moral skew angle is: .theta.=60.3.degree..
[0430] As confirmation, it can be observed that, according to Eqs.
(146) and (147), s and {circumflex over (k)} are, indeed, unit
vectors. For example, according to Eq. (147), the {circumflex over
(k)}-vector length is
k ^ = 36 40 + 4 40 = 1 ( 149 ) ##EQU00046##
[0431] Section 8: Example Computer Program Product Embodiments
[0432] As used herein, the term module might describe a given unit
of functionality that can be performed in accordance with one or
more embodiments of the present invention. As used herein, a module
might be implemented utilizing any form of hardware, software, or a
combination thereof. For example, one or more processors,
controllers, ASICs, PLAs, PALs, CPLDs, FPGAs, logical components,
software routines or other mechanisms might be implemented to make
up a module. In implementation, the various modules described
herein might be implemented as discrete modules or the functions
and features described can be shared in part or in total among one
or more modules. In other words, as would be apparent to one of
ordinary skill in the art after reading this description, the
various features and functionality described herein may be
implemented in any given application and can be implemented in one
or more separate or shared modules in various combinations and
permutations. Even though various features or elements of
functionality may be individually described or claimed as separate
modules, one of ordinary skill in the art will understand that
these features and functionality can be shared among one or more
common software and hardware elements, and such description shall
not require or imply that separate hardware or software components
are used to implement such features or functionality.
[0433] Where components or modules of the invention are implemented
in whole or in part using software, in one embodiment, these
software elements can be implemented to operate with a computing or
processing module capable of carrying out the functionality
described with respect thereto. One such example computing module
is shown in FIG. 49. Various embodiments are described in terms of
this example-computing module 9500. After reading this description,
it will become apparent to a person skilled in the relevant art how
to implement the invention using other computing modules or
architectures.
[0434] Referring now to FIG. 49, computing module 9500 may
represent, for example, computing or processing capabilities found
within desktop, laptop and notebook computers; hand-held computing
devices (PDA's, smart phones, cell phones, palmtops, etc.);
mainframes, supercomputers, workstations or servers; or any other
type of special-purpose or general-purpose computing devices as may
be desirable or appropriate for a given application or environment.
Computing module 9500 might also represent computing capabilities
embedded within or otherwise available to a given device. For
example, a computing module might be found in other electronic
devices such as, for example, digital cameras, navigation systems,
cellular telephones, portable computing devices, modems, routers,
WAPs, terminals and other electronic devices that might include
some form of processing capability.
[0435] Computing module 9500 might include, for example, one or
more processors, controllers, control modules, or other processing
devices, such as a processor 9504. Processor 9504 might be
implemented using a general-purpose or special-purpose processing
engine such as, for example, a microprocessor, controller, or other
control logic. In the illustrated example, processor 9504 is
connected to a bus 9502, although any communication medium can be
used to facilitate interaction with other components of computing
module 9500 or to communicate externally.
[0436] Computing module 9500 might also include one or more memory
modules, simply referred to herein as main memory 9508. For
example, preferably random access memory (RAM) or other dynamic
memory, might be used for storing information and instructions to
be executed by processor 9504. Main memory 9508 might also be used
for storing temporary variables or other intermediate information
during execution of instructions to be executed by processor 9504.
Computing module 9500 might likewise include a read only memory
("ROM") or other static storage device coupled to bus 9502 for
storing static information and instructions for processor 9504.
[0437] The computing module 9500 might also include one or more
various forms of information storage mechanism 9510, which might
include, for example, a media drive 9512 and a storage unit
interface 9520. The media drive 9512 might include a drive or other
mechanism to support fixed or removable storage media 9514. For
example, a hard disk drive, a floppy disk drive, a magnetic tape
drive, an optical disk drive, a CD or DVD drive (R or RW), or other
removable or fixed media drive might be provided. Accordingly,
storage media 9514 might include, for example, a hard disk, a
floppy disk, magnetic tape, cartridge, optical disk, a CD or DVD,
or other fixed or removable medium that is read by, written to or
accessed by media drive 9512. As these examples illustrate, the
storage media 9514 can include a computer usable storage medium
having stored therein computer software or data.
[0438] In alternative embodiments, information storage mechanism
9510 might include other similar instrumentalities for allowing
computer programs or other instructions or data to be loaded into
computing module 9500. Such instrumentalities might include, for
example, a fixed or removable storage unit 9522 and an interface
9520. Examples of such storage units 9522 and interfaces 9520 can
include a program cartridge and cartridge interface, a removable
memory (for example, a flash memory or other removable memory
module) and memory slot, a PCMCIA slot and card, and other fixed or
removable storage units 9522 and interfaces 9520 that allow
software and data to be transferred from the storage unit 9522 to
computing module 9500.
[0439] Computing module 9500 might also include a communications
interface 9524. Communications interface 9524 might be used to
allow software and data to be transferred between computing module
9500 and external devices. Examples of communications interface
9524 might include a modem or softmodem, a network interface (such
as an Ethernet, network interface card, WiMedia, IEEE 802.XX or
other interface), a communications port (such as for example, a USB
port, IR port, RS232 port Bluetooth.RTM. interface, or other port),
or other communications interface. Software and data transferred
via communications interface 9524 might typically be carried on
signals, which can be electronic, electromagnetic (which includes
optical) or other signals capable of being exchanged by a given
communications interface 4924. These signals might be provided to
communications interface 9524 via a channel 9528. This channel 9528
might carry signals and might be implemented using a wired or
wireless communication medium. Some examples of a channel might
include a phone line, a cellular link, an RF link, an optical link,
a network interface, a local or wide area network, and other wired
or wireless communications channels.
[0440] In this document, the terms "computer program medium" and
"computer usable medium" are used to generally refer to media such
as, for example, memory 9508, storage unit 9520, media 9514, and
channel 9528. These and other various forms of computer program
media or computer usable media may be involved in carrying one or
more sequences of one or more instructions to a processing device
for execution. Such instructions embodied on the medium, are
generally referred to as "computer program code" or a "computer
program product" (which may be grouped in the form of computer
programs or other groupings). When executed, such instructions
might enable the computing module 9500 to perform features or
functions of the present invention as discussed herein.
[0441] While various embodiments of the present invention have been
described above, it should be understood that they have been
presented by way of example only, and not of limitation. Likewise,
the various diagrams may depict an example architectural or other
configuration for the invention, which is done to aid in
understanding the features and functionality that can be included
in the invention. The invention is not restricted to the
illustrated example architectures or configurations, but the
desired features can be implemented using a variety of alternative
architectures and configurations. Indeed, it will be apparent to
one of skill in the art how alternative functional, logical or
physical partitioning and configurations can be implemented to
implement the desired features of the present invention. Also, a
multitude of different constituent module names other than those
depicted herein can be applied to the various partitions.
Additionally, with regard to flow diagrams, operational
descriptions and method claims, the order in which the steps are
presented herein shall not mandate that various embodiments be
implemented to perform the recited functionality in the same order
unless the context dictates otherwise.
[0442] Although the invention is described above in terms of
various exemplary embodiments and implementations, it should be
understood that the various features, aspects and functionality
described in one or more of the individual embodiments are not
limited in their applicability to the particular embodiment with
which they are described, but instead can be applied, alone or in
various combinations, to one or more of the other embodiments of
the invention, whether or not such embodiments are described and
whether or not such features are presented as being a part of a
described embodiment. Thus, the breadth and scope of the present
invention should not be limited by any of the above-described
exemplary embodiments.
[0443] Terms and phrases used in this document, and variations
thereof, unless otherwise expressly stated, should be construed as
open ended as opposed to limiting. As examples of the foregoing:
the term "including" should be read as meaning "including, without
limitation" or the like; the term "example" is used to provide
exemplary instances of the item in discussion, not an exhaustive or
limiting list thereof; the terms "a" or "an" should be read as
meaning "at least one," "one or more" or the like; and adjectives
such as "conventional," "traditional," "normal," "standard,"
"known" and terms of similar meaning should not be construed as
limiting the item described to a given time period or to an item
available as of a given time, but instead should be read to
encompass conventional, traditional, normal, or standard
technologies that may be available or known now or at any time in
the future. Likewise, where this document refers to technologies
that would be apparent or known to one of ordinary skill in the
art, such technologies encompass those apparent or known to the
skilled artisan now or at any time in the future.
[0444] The presence of broadening words and phrases such as "one or
more," "at least," "but not limited to" or other like phrases in
some instances shall not be read to mean that the narrower case is
intended or required in instances where such broadening phrases may
be absent. The use of the term "module" does not imply that the
components or functionality described or claimed as part of the
module are all configured in a common package. Indeed, any or all
of the various components of a module, whether control logic or
other components, can be combined in a single package or separately
maintained and can further be distributed in multiple groupings or
packages or across multiple locations.
[0445] Additionally, the various embodiments set forth herein are
described in terms of exemplary block diagrams, flow charts and
other illustrations. As will become apparent to one of ordinary
skill in the art after reading this document, the illustrated
embodiments and their various alternatives can be implemented
without confinement to the illustrated examples. For example, block
diagrams and their accompanying description should not be construed
as mandating a particular architecture or configuration.
* * * * *